Daily Papers

Sparse autoencoders (SAEs) decompose language model activations into interpretable features, but existing methods reveal only which features activate, not which change model outputs when amplified. We introduce Control Reinforcement Learning (CRL), which trains a policy to select SAE features for steering at each token, producing interpretable intervention logs: the learned policy identifies features that change model outputs when amplified. Adaptive Feature Masking encourages diverse feature discovery while preserving singlefeature interpretability. The framework yields new analysis capabilities: branch point tracking locates tokens where feature choice determines output correctness; critic trajectory analysis separates policy limitations from value estimation errors; layer-wise comparison reveals syntactic features in early layers and semantic features in later layers. On Gemma 2 2B across MMLU, BBQ, GSM8K, HarmBench, and XSTest, CRL achieves improvements while providing per-token intervention logs. These results establish learned feature steering as a mechanistic interpretability tool that complements static feature analysis with dynamic intervention probes

Large Language Models (LLMs) offer a promising basis for creating agents that can tackle complex tasks through iterative environmental interaction. Existing methods either require these agents to mimic expert-provided trajectories or rely on definitive environmental feedback for reinforcement learning which limits their application to specific scenarios like gaming or code generation. This paper introduces a novel training method for LLM-based agents using weakly supervised signals from a critic LLM, bypassing the need for expert trajectories or definitive feedback. Our agents are trained in iterative manner, where they initially generate trajectories through environmental interaction. Subsequently, a critic LLM selects a subset of good trajectories, which are then used to update the agents, enabling them to generate improved trajectories in the next iteration. Extensive tests on the API-bank dataset show consistent improvement in our agents' capabilities and comparable performance to GPT-4, despite using open-source models with much fewer parameters.

Critique-guided reinforcement learning (RL) has emerged as a powerful paradigm for training LLM agents by augmenting sparse outcome rewards with natural-language feedback. However, current methods often rely on static or offline critic models, which fail to adapt as the policy evolves. In on-policy RL, the agent's error patterns shift over time, causing stationary critics to become stale and providing feedback of diminishing utility. To address this, we introduce ECHO (Evolving Critic for Hindsight-Guided Optimization)}, a framework that jointly optimizes the policy and critic through a synchronized co-evolutionary loop. ECHO utilizes a cascaded rollout mechanism where the critic generates multiple diagnoses for an initial trajectory, followed by policy refinement to enable group-structured advantage estimation. We address the challenge of learning plateaus via a saturation-aware gain shaping objective, which rewards the critic for inducing incremental improvements in high-performing trajectories. By employing dual-track GRPO updates, ECHO ensures the critic's feedback stays synchronized with the evolving policy. Experimental results show that ECHO yields more stable training and higher long-horizon task success across open-world environments.

Outcome-supervised search agents learn when and how to retrieve evidence, but terminal rewards neither localize intermediate errors nor redirect an ongoing trajectory before those errors compound. Treating corrective feedback as a learned in-trajectory intervention couples the two roles: the agent must decide when to request and use feedback, while the critic must infer useful corrections from outcome-confounded rollouts whose failure patterns shift as the agent improves. We introduce CAFE (Coupled Agent--Feedback Evolution), a framework in which a shared-parameter model alternates between search-agent and critic roles. CAFE initializes feedback-conditioned recovery from trajectories built around the base agent's own failures, then couples online and offline optimization. During online RL, a comparative feedback estimate uses a prompt-level call--skip success gap to shape request returns, while feedback-aware advantage shaping reweights token advantages before and after feedback. Offline, rollout-derived preference optimization learns feedback from matched successful and unsuccessful trajectories. On seven agentic search benchmarks, CAFE outperforms the evaluated RL-based search agents on average, retains its gains across all six out-of-domain benchmarks, and reduces answer-level hallucinations. One-sided ablations show that improving only the agent or only the critic eventually plateaus, whereas alternating the two updates continues to improve performance. These findings suggest that a self-improving search agent needs feedback that co-evolves with the policy it guides.

Agentic code review in terminal-based environments enables early feedback during local development before pull request creation. However, existing evaluations remain performance-centric and fail to capture the dynamic behaviors of repository-grounded agentic reviewers. Understanding these behaviors is critical for identifying how agentic reviewers succeed, fail, and incur hidden operational costs in practice. Then, we analyze the reviewers' behavior based on their trajectories. Our results show that agentic reviewers achieve higher review precision but incur substantial exploration and validation overhead, while successful reviews are associated with stronger planning and less downstream validation. These findings highlight the potential benefits of trajectory-aware and cost-sensitive evaluation of future agentic code review systems.

End-to-end code agent training is resource-intensive and plateaus on the strategy-level reasoning needed to resolve code issues, since jointly optimizing code-level execution and strategy-level reasoning leaves the latter underdeveloped. Instead, we freeze the agent and add a critic model to supply that signal. Prior code critics are post-hoc, scoring completed trajectories rather than steering the agent; we instead train a small critic that provides intra-trajectory feedback via Supervised Fine-Tuning. On SWE-bench Verified, a critic trained on CWM-32B trajectories transfers to two unseen agents (gains of +3.0 to +3.8 points), and adding target-agent trajectories to the corpus increases the gain to +3.8 on CWM-32B and +4.4 to +5.2 on two Qwen agents, at 30-92x lower critic cost than a strong teacher. On Qwen3-Next-80B-A3B, the critic-guided system is both more accurate (25.2% vs. 20.8%) and cheaper (\0.04 vs. 0.11) than the agent alone, because the critic also shortens trajectories. Our results show that a small, well-trained critic is a practical complement to scaling agent training. Code: https://github.com/shubhamrgandhi/critic-training. Data and models: https://huggingface.co/collections/shubhamrgandhi/critic-training-for-code-agents

We consider the problem of learning good trajectories for manipulation tasks. This is challenging because the criterion defining a good trajectory varies with users, tasks and environments. In this paper, we propose a co-active online learning framework for teaching robots the preferences of its users for object manipulation tasks. The key novelty of our approach lies in the type of feedback expected from the user: the human user does not need to demonstrate optimal trajectories as training data, but merely needs to iteratively provide trajectories that slightly improve over the trajectory currently proposed by the system. We argue that this co-active preference feedback can be more easily elicited from the user than demonstrations of optimal trajectories, which are often challenging and non-intuitive to provide on high degrees of freedom manipulators. Nevertheless, theoretical regret bounds of our algorithm match the asymptotic rates of optimal trajectory algorithms. We demonstrate the generalizability of our algorithm on a variety of grocery checkout tasks, for whom, the preferences were not only influenced by the object being manipulated but also by the surrounding environment.For more details and a demonstration video, visit: \url{http://pr.cs.cornell.edu/coactive}

Recent approaches to reinforcement learning (RL) post-training for large language models increasingly remove the critic to reduce training instability and memory overhead. Even where a critic is trained, it is discarded once training ends, although it has learned to predict outcomes. We revisit this trend and show that a pretrained critic's ability to predict future outcomes can make it a valuable asset for efficient long-horizon reasoning. First, we find that instability in critic-based RL for long chain-of-thought reasoning is largely an optimization artifact: keeping policy updates small and low in variance restores stable convergence. Second, a well-pretrained critic estimates the posterior probability of eventual success from later trajectory states and unfinished prefixes. Its predictions provide outcome-derived, dense, per-prefix learning signals that, during policy optimization, require neither completed rollouts, step-level annotations, nor external reward labels. Building on this insight, we introduce Reward-Free Policy Optimization (RFPO), which repurposes a single calibrated, frozen critic as a rollout-level reward, a value baseline for generalized advantage estimation, and a success forecaster for unfinished prefixes. We further show that binarizing the debiased score stops the policy from exploiting the critic's length bias. Binarized, RFPO matches supervised PPO without a single label in the training loop, while cutting compute and memory overhead. This makes RFPO well suited to long-horizon reasoning tasks, where outcomes arrive late and generation dominates cost: because rollouts can be rewarded before they finish, training no longer has to pay for waiting on every trajectory to complete. Our findings challenge the prevailing critic-free paradigm and establish critic-based, reward-free optimization as a scalable and computationally efficient path for LLM post-training.

While Large Vision-Language Models (LVLMs) have significantly advanced GUI agents' capabilities in parsing textual instructions, interpreting screen content, and executing tasks, a critical challenge persists: the irreversibility of agent operations-where a single erroneous action can trigger catastrophic deviations. To address this, we propose the GUI Action Critic's Data Flywheel System (GAIA), a training framework that enables the models to have iterative critic capabilities, which are used to improve the Test-Time Scaling (TTS) of basic GUI agents' performance. Specifically, we train an Intuitive Critic Model (ICM) using positive and negative action examples from a base agent first. This critic evaluates the immediate correctness of the agent's intended actions, thereby selecting operations with higher success probability. Then, the initial critic guides agent actions to collect refined positive/negative samples, initiating the self-improving cycle. The augmented data then trains a second-round critic with enhanced discernment capability. We conduct experiments on various datasets and demonstrate that the proposed ICM can improve the test-time performance of various closed-source and open-source models, and the performance can be gradually improved as the data is recycled. The code, dataset, and accompanying datasheet will be publicly released at https://github.com/SeerRay-Lab/GAIA.

Tool-Integrated Reasoning (TIR) with search engines enables large language models to iteratively retrieve up-to-date external knowledge, enhancing adaptability and generalization in complex question-answering tasks. However, existing search agent pipelines typically depend on reinforcement learning based optimization, which often suffers from sparse outcome rewards, leading to inefficient exploration and unstable training. We introduce CriticSearch, a fine-grained credit-assignment framework that supplies dense, turn-level feedback via a retrospective critic mechanism. During training, a frozen, asymmetric critique LLM retrospectively evaluates each turn using privileged information from the full trajectory and gold answers, converting these assessments into stable, dense rewards that guide policy improvement. Experimental results across diverse multi-hop reasoning benchmarks demonstrate that CriticSearch consistently outperforms existing baselines, achieving faster convergence, improved training stability, and higher performance.

Offline reinforcement learning is typically analyzed under process-level reward supervision, yet many sequential decision datasets record only trajectory-level outcomes. We develop a statistical theory for offline policy optimization from such outcome-level supervision. We first study the canonical setting where the target remains the expected cumulative reward, but each offline trajectory provides only a scalar label whose conditional mean is the cumulative return. We propose OPAC, a pessimistic actor-critic algorithm that learns a latent reward model and optimizes a policy from trajectory-level labels. We prove a high-probability guarantee of order widetilde O(H^2C_{sa(π^star)/n}) and a matching lower bound, characterizing the sharp statistical cost of replacing process-level rewards with one trajectory-level label. We then extend the principle to preference-based feedback, preserving the leading horizon and concentrability dependence up to preference-model constants. Finally, we study generalized outcome-based offline RL, where both the supervision and the objective are trajectory-level quantities induced by a nonlinear aggregation of latent per-step rewards. This problem is not learnable in general: for all-success objectives, any offline learner may require Ω(2^H) trajectories even with deterministic transitions and constant concentrability. We then identify a tractable regime through two structural coefficients, κ_μ(σ) and χ_μ(σ), capturing information loss in outcome aggregation and generalized Bellman updates, under which generalized OPAC achieves polynomial sample complexity. Together, our results delineate when outcome-level supervision enables sample-efficient offline control and when missing process-level rewards create fundamental statistical barriers.

Human-Scene Interaction (HSI) seeks to generate realistic human behaviors within complex environments, yet it faces significant challenges in handling long-horizon, high-level tasks and generalizing to unseen scenes. To address these limitations, we introduce FantasyHSI, a novel HSI framework centered on video generation and multi-agent systems that operates without paired data. We model the complex interaction process as a dynamic directed graph, upon which we build a collaborative multi-agent system. This system comprises a scene navigator agent for environmental perception and high-level path planning, and a planning agent that decomposes long-horizon goals into atomic actions. Critically, we introduce a critic agent that establishes a closed-loop feedback mechanism by evaluating the deviation between generated actions and the planned path. This allows for the dynamic correction of trajectory drifts caused by the stochasticity of the generative model, thereby ensuring long-term logical consistency. To enhance the physical realism of the generated motions, we leverage Direct Preference Optimization (DPO) to train the action generator, significantly reducing artifacts such as limb distortion and foot-sliding. Extensive experiments on our custom SceneBench benchmark demonstrate that FantasyHSI significantly outperforms existing methods in terms of generalization, long-horizon task completion, and physical realism. Ours project page: https://fantasy-amap.github.io/fantasy-hsi/

A key strength of Proximal Policy Optimization (PPO) is its learned critic, which uses historical trajectories collected during reinforcement learning to estimate expected returns and reduce policy-gradient variance. However, we find that the critic is also a major source of instability in reinforcement learning for large language models (LLMs). We identify two critic failure modes that destabilize PPO. First, filtering truncated rollouts from both actor and critic shifts the policy objective to reward conditioned on completion, allowing truncation to increase even as conditional reward improves. Second, heterogeneous return noise can cause high-variance prompts to dominate critic updates in finite batches. We introduce EasyPPO to address these failures. Actor-only overlong filtering trains the critic on returns from both completed and truncated rollouts. Noise-normalized critic regression weights each prompt's critic loss by the inverse standard deviation of its sampled returns, balancing noise contributions across prompts. Moderately smaller critic mini-batches confine outlier influence to fewer rollouts during gradient clipping. Across continuous-reward coding on FrontierCS, binary-reward mathematical reasoning on AIME24, and multi-turn search on Search-R1, EasyPPO remains stable throughout the full training horizon and consistently outperforms vanilla PPO, VAPO, and HL-Gauss PPO. Its best validation scores show relative gains of 14.89%, 2.28%, and 9.47% over PPO, respectively.

State-of-the-art large language models (LLMs) exhibit impressive problem-solving capabilities but may struggle with complex reasoning and factual correctness. Existing methods harness the strengths of chain-of-thought and retrieval-augmented generation (RAG) to decompose a complex problem into simpler steps and apply retrieval to improve factual correctness. These methods work well on straightforward reasoning tasks but often falter on challenging tasks such as competitive programming and mathematics, due to frequent reasoning errors and irrelevant knowledge retrieval. To address this, we introduce Critic-guided planning with Retrieval-augmentation, CR-Planner, a novel framework that leverages fine-tuned critic models to guide both reasoning and retrieval processes through planning. CR-Planner solves a problem by iteratively selecting and executing sub-goals. Initially, it identifies the most promising sub-goal from reasoning, query generation, and retrieval, guided by rewards given by a critic model named sub-goal critic. It then executes this sub-goal through sampling and selecting the optimal output based on evaluations from another critic model named execution critic. This iterative process, informed by retrieved information and critic models, enables CR-Planner to effectively navigate the solution space towards the final answer. We employ Monte Carlo Tree Search to collect the data for training the critic models, allowing for a systematic exploration of action sequences and their long-term impacts. We validate CR-Planner on challenging domain-knowledge-intensive and reasoning-heavy tasks, including competitive programming, theorem-driven math reasoning, and complex domain retrieval problems. Our experiments demonstrate that CR-Planner significantly outperforms baselines, highlighting its effectiveness in addressing challenging problems by improving both reasoning and retrieval.

Actor-critic algorithms have become a cornerstone in reinforcement learning (RL), leveraging the strengths of both policy-based and value-based methods. Despite recent progress in understanding their statistical efficiency, no existing work has successfully learned an epsilon-optimal policy with a sample complexity of O(1/epsilon^2) trajectories with general function approximation when strategic exploration is necessary. We address this open problem by introducing a novel actor-critic algorithm that attains a sample-complexity of O(dH^5 log|A|/epsilon^2 + d H^4 log|F|/ epsilon^2) trajectories, and accompanying T regret when the Bellman eluder dimension d does not increase with T at more than a log T rate. Here, F is the critic function class, A is the action space, and H is the horizon in the finite horizon MDP setting. Our algorithm integrates optimism, off-policy critic estimation targeting the optimal Q-function, and rare-switching policy resets. We extend this to the setting of Hybrid RL, showing that initializing the critic with offline data yields sample efficiency gains compared to purely offline or online RL. Further, utilizing access to offline data, we provide a non-optimistic provably efficient actor-critic algorithm that only additionally requires N_{off} geq c_{off}^*dH^4/epsilon^2 in exchange for omitting optimism, where c_{off}^* is the single-policy concentrability coefficient and N_{off} is the number of offline samples. This addresses another open problem in the literature. We further provide numerical experiments to support our theoretical findings.

Reinforcement mid-training lets language models learn internal thoughts from unlabeled text, but efficient token-level credit assignment remains challenging. Existing group-relative methods require costly repeated generation. Learned critics offer single-rollout feedback, but accurate return prediction alone does not ensure reliable policy updates. Our analysis shows how training--inference mismatch and PPO clipping prevent a common offset in advantage estimates from cancelling out, introducing additional update drift. We propose , a twin-critic method that calibrates token-level advantages from a single generated trajectory. After warmup and held-out qualification, the critics provide two advantage estimates, combined using action-dependent weights learned through a conditional-moment saddle-point objective. This objective brings the average advantage at each prefix toward zero, while a signal-retention constraint prevents the correction from erasing the learning signal. Sharing information across text positions avoids repeated sampling of each prefix. Theoretically, we characterize optimal mixing under the signal-retention constraint and establish an upper bound on residual mean-induced drift. Experiments show that, compared with the state-of-the-art critic-free method, improves mean benchmark performance by 7.8\% and reduces mean training-step time by up to 63.4\%.

With VLM-powered computer-using agents (CUAs) becoming increasingly capable at graphical user interface (GUI) navigation and manipulation, reliable step-level decision-making has emerged as a key bottleneck for real-world deployment. In long-horizon workflows, errors accumulate quickly and irreversible actions can cause unintended consequences, motivating critic models that assess each action before execution. While critic models offer a promising solution, their effectiveness is hindered by the lack of diverse, high-quality GUI feedback data and public critic benchmarks for step-level evaluation in computer use. To bridge these gaps, we introduce OS-Oracle that makes three core contributions: (1) a scalable data pipeline for synthesizing cross-platform GUI critic data; (2) a two-stage training paradigm combining supervised fine-tuning (SFT) and consistency-preserving group relative policy optimization (CP-GRPO); (3) OS-Critic Bench, a holistic benchmark for evaluating critic model performance across Mobile, Web, and Desktop platforms. Leveraging this framework, we curate a high-quality dataset containing 310k critic samples. The resulting critic model, OS-Oracle-7B, achieves state-of-the-art performance among open-source VLMs on OS-Critic Bench, and surpasses proprietary models on the mobile domain. Furthermore, when serving as a pre-critic, OS-Oracle-7B improves the performance of native GUI agents such as UI-TARS-1.5-7B in OSWorld and AndroidWorld environments. The code is open-sourced at https://github.com/numbmelon/OS-Oracle.

Large language model (LLM) agents are increasingly deployed in long-horizon, interactive, and stateful environments. In these settings, a single wrong action, such as refunding the wrong purchase, can cause irreversible task failure and must be intercepted before execution. Such failures may not appear in every single run, but can emerge across repeated trials, making reliability across steps and trials critical. However, ensuring agentic reliability is challenging: even frontier LLMs struggle to explain why an action may be wrong, especially in long, intertwined trajectories governed by domain-specific policies. Much recent work relies on prompt-based critique agents, while optimization-based methods lack a systematic way to produce rich verification rationales for training. We address this gap with CAST, a critique-aware training framework that converts sparse task outcomes into action-level supervision for critique learning and policy optimization. CAST analyzes agent trajectories to synthesize structured rationales explaining action validity under partial observability. The resulting critique model is used to construct critique-aware training data for optimizing the policy model. Fine-tuning Qwen3-family models on dynamic tool-calling benchmarks, CAST improves reliability across domains, outperforming GPT-OSS-120B by over 10% pass^4 on Retail tasks and yielding an additional 9% improvement on Telehealth in an out-of-domain setting. These results demonstrate that critique-aware training improves the robustness of LLM agents in realistic dynamic environments.

In this paper, we study the role of the critic in actor--critic for entropy-regularized, finite, discounted environments. We establish that, when the critic is exact, using the latter as a baseline is a variance-reduction method in a strong sense. In this case, actor--critic with stochastic gradients matches the sample complexity of deterministic policy gradient, reaching an ε-optimal regularized value with O(log(1/ε)) samples. In practice, the critic is learned alongside the actor: the variance of the actor update is then influenced by the critic's variance and bias. Specifically, when the critic has a sufficiently small error, the variance reduction and rapid convergence are preserved. This suggests to learn the critic first, keeping it up to date after each actor update, underscoring the crucial role of accurate critic estimation in actor--critic methods.

Policy gradient methods are reinforcement learning algorithms that adapt a parameterized policy by following a performance gradient estimate. Conventional policy gradient methods use Monte-Carlo techniques to estimate the gradient, which tend to have high variance, requiring many samples and resulting in slow convergence. We first propose a Bayesian framework for policy gradient, based on modeling the policy gradient as a Gaussian process. This reduces the number of samples needed to obtain accurate gradient estimates. Moreover, estimates of the natural gradient and a measure of the uncertainty in the gradient estimates, namely, the gradient covariance, are provided at little extra cost. Since the proposed framework considers system trajectories as its basic observable unit, it does not require the dynamics within trajectories to be of any particular form, and can be extended to partially observable problems. On the downside, it cannot exploit the Markov property when the system is Markovian. To address this, we supplement our Bayesian policy gradient framework with a new actor-critic learning model in which a Bayesian class of non-parametric critics, based on Gaussian process temporal difference learning, is used. Such critics model the action-value function as a Gaussian process, allowing Bayes rule to be used to compute the posterior distribution over action-value functions, conditioned on the observed data. Appropriate choices of the policy parameterization and of the prior covariance (kernel) between action-values yield closed-form expressions for the posterior of the gradient of the expected return with respect to the policy parameters. We perform detailed experimental comparisons of the proposed Bayesian policy gradient and actor-critic algorithms with classic Monte-Carlo based policy gradient methods, on a number of reinforcement learning problems.

Multi-Agent Reinforcement Learning (MARL) is increasingly deployed in safety-critical domains, yet methods for interpretable failure detection and attribution remain underdeveloped. We introduce a two-stage gradient-based framework that provides interpretable diagnostics for three critical failure analysis tasks: (1) detecting the true initial failure source (Patient-0); (2) validating why non-attacked agents may be flagged first due to domino effects; and (3) tracing how failures propagate through learned coordination pathways. Stage 1 performs interpretable per-agent failure detection via Taylor-remainder analysis of policy-gradient costs, declaring an initial Patient-0 candidate at the first threshold crossing. Stage 2 provides validation through geometric analysis of critic derivatives-first-order sensitivity and directional second-order curvature aggregated over causal windows to construct interpretable contagion graphs. This approach explains "downstream-first" detection anomalies by revealing pathways that amplify upstream deviations. Evaluated across 500 episodes in Simple Spread (3 and 5 agents) and 100 episodes in StarCraft II using MADDPG and HATRPO, our method achieves 88.2-99.4% Patient-0 detection accuracy while providing interpretable geometric evidence for detection decisions. By moving beyond black-box detection to interpretable gradient-level forensics, this framework offers practical tools for diagnosing cascading failures in safety-critical MARL systems.

Planning with learned world models combines online trajectory optimization with learned value and policy functions for high-dimensional control. Because the planner determines the experience used for learning, while the learned critic and actor in turn score and propose future plans, planning and learning form a closed feedback loop. TD-MPC is a prominent instance of this design. Recent policy-constrained variants strengthen one part of the loop by aligning the learned policy with planner behavior. We introduce PL-MPC (Planning-Learning MPC), which additionally modifies critic supervision and planner terminal-value estimation. Hybrid multi-step TD targets expose critic updates to more realized rewards before bootstrapping; disagreement-aware terminal estimates reduce the influence of uncertain critic values during MPPI planning; and return-weighted actor distillation emphasizes planner-executed actions from high-return episodes. The world-model architecture and MPPI optimizer are otherwise unchanged. On HumanoidBench, the largest gains occur on balance-hard, where Total Average Return (TAR) increases from 98pm18 to 387pm255, and hurdle, from 199pm13 to 466pm200; performance across the broader benchmark remains task dependent, and PL-MPC remains competitive on DMControl. Controlled ablations show different component interactions across the two tasks. We further demonstrate zero-shot sim-to-real transfer on wrench-nut alignment with a 7-DoF KUKA IIWA14, obtaining higher observed success than TD-M(PC)^2 on the training object size and two unseen sizes. Code and data will be available at: https://pl-mpc-humanoid.github.io.

Reinforcement learning (RL) post-training of Vision-Language-Action (VLA) models has shown strong promise for robotic manipulation. Among RL methods, critic-based approaches rely on a value estimator that predominantly operates on single-frame observations or single-frame VLM backbone latents, which is a fundamental mismatch with the partially observable nature of robot control. A naive approach to incorporate observation history into the critic incurs exponential complexity with high-dimensional visual space, and still fails because pure scalar-return regression provides insufficient supervision for learning cross-temporal dynamics. We identify the root cause as a state approximation problem: without an explicit world modeling objective, the critic's representation cannot capture the temporal structure needed for accurate value estimation. To address this, we propose the World Critic Model (WCM), built on a lightweight LeJEPA architecture; WCM jointly predicts future latent state and estimates values, such that the critic's representation is explicitly trained to capture temporal dynamics rather than merely regress scalar returns. WCM integrates seamlessly into both on-policy and off-policy training pipelines and is compatible with state-of-the-art VLA backbones including Pi0, Pi0.5, and OpenVLA-OFT. Extensive experiments on 149 tasks across four benchmarks demonstrate that WCM consistently achieves state-of-the-art performance in both in-distribution and out-of-distribution settings, with particularly strong generalization gains. We further validate WCM on seven real-world manipulation tasks using OpenVLA-OFT and Pi0.5 with off-policy RL, confirming stable deployment across diverse settings.

Trajectory prediction models in autonomous driving are vulnerable to perturbations from non-causal agents whose actions should not affect the ego-agent's behavior. Such perturbations can lead to incorrect predictions of other agents' trajectories, potentially compromising the safety and efficiency of the ego-vehicle's decision-making process. Motivated by this challenge, we propose Causal tRajecTory predICtion (CRiTIC), a novel model that utilizes a Causal Discovery Network to identify inter-agent causal relations over a window of past time steps. To incorporate discovered causal relationships, we propose a novel Causal Attention Gating mechanism to selectively filter information in the proposed Transformer-based architecture. We conduct extensive experiments on two autonomous driving benchmark datasets to evaluate the robustness of our model against non-causal perturbations and its generalization capacity. Our results indicate that the robustness of predictions can be improved by up to 54% without a significant detriment to prediction accuracy. Lastly, we demonstrate the superior domain generalizability of the proposed model, which achieves up to 29% improvement in cross-domain performance. These results underscore the potential of our model to enhance both robustness and generalization capacity for trajectory prediction in diverse autonomous driving domains. Further details can be found on our project page: https://ehsan-ami.github.io/critic.

The overestimation bias is one of the major impediments to accurate off-policy learning. This paper investigates a novel way to alleviate the overestimation bias in a continuous control setting. Our method---Truncated Quantile Critics, TQC,---blends three ideas: distributional representation of a critic, truncation of critics prediction, and ensembling of multiple critics. Distributional representation and truncation allow for arbitrary granular overestimation control, while ensembling provides additional score improvements. TQC outperforms the current state of the art on all environments from the continuous control benchmark suite, demonstrating 25% improvement on the most challenging Humanoid environment.

Deciding whether a trajectory actually fulfills its instruction governs how we measure computer-use agents on long-horizon graphical-user-interface tasks and how we train them with reinforcement learning. This judgment has long relied on rule-based evaluation, which struggles to align with human intention and goes stale when an app updates or its online content drifts. Existing model-based judges attempt to address these problems but still leave a performance gap to the rule-based evaluation. We propose the SeekJudge framework, in which four role-specialized agents, a Condense, a Ground, a Seek and an Analyze agent, reach a verdict through a Seek--Analyze loop over the trajectory. A seed-calibrated distillation pipeline trains one specialized 9B model to serve as the shared backbone for all four agents. Measured by downstream success rate on held-out RL test goals, SeekJudge is the first practical model-based reward to match or surpass native rule-based supervision in online RL. Beyond accuracy, SeekJudge provides step-level judgments, runs far cheaper than a closed-source large model, and keeps a small per-call context that scales to much longer trajectories. We further contribute a general architectural improvement to the reward server that speeds up judging in RL. Together these make model-based reward a practical drop-in for rule-based supervision in CUA reinforcement learning.

Multimodal large language models exhibit capabilities on reasoning tasks, yet often produce flawed intermediate steps while yielding correct final answers. This behavior undermines interpretability and reliability, suggesting reliance on spurious shortcuts rather than faithful reasoning. Although efforts have explored step-level supervision, distinguishing decisive steps from redundant ones remains challenging. We propose O^2-CritiCuRL, a novel curriculum reinforcement learning framework that introduces critical-step awareness through an iterative offline-online paradigm. In the offline stage, O^2-CritiCuRL conducts multi-rollout analysis over step-annotated trajectories to estimate step-level importance, allowing the framework to distill critical reasoning steps and filter out redundant ones. In the online stage, we employ a progressive step-level reinforcement learning strategy, where truncated chains guide the model to infer missing steps and refine its reasoning, thereby sharpening its focus on critical steps and overcoming the limitations of static supervision. Extensive experiments on multimodal reasoning benchmarks show that our method achieves state-of-the-art performance while delivering superior training and inference efficiency. Code is available at https://github.com/kk0013/CritiCuRL.

We propose Q-Guided Value-Gradient Matching (Q-VGM), an off-policy reinforcement learning method for a central difficulty in fine-tuning flow-matching vision-language-action (VLA) policies: improving an expressive flow-matching action expert with a learned Q-function. Effective improvement must exploit the critic's first-order signal nabla_A Q, yet flow policies make this hard: backpropagating values through the multi-step denoising chain is unstable at VLA scale, and the tractable action likelihoods required by policy gradients are unavailable under iterative denoising. Existing value-based methods therefore backpropagate through the full chain, use the critic only for test-time selection or guidance, or distill critic-improved actions as terminal labels that never supervise the velocity field. Q-VGM instead casts policy improvement as optimal control over the denoising dynamics, where the optimal residual velocity is the gradient of a denoising-time value function: clean-action estimates improved by iterative Q-gradient ascent with keep-best selection are converted into residual velocity targets that directly supervise the velocity field -- no action likelihoods, no backpropagation through the denoising chain, fully offline on a fixed replay buffer, and no critic at inference time. The critic is an action-sensitive stepwise IQL critic on compact latent states from the frozen VLA backbone. This enables a few-shot-initialization, learn-from-experience paradigm: starting from a few-shot-SFT π_{0.5} policy, Q-VGM improves the policy from its own rollouts without additional expert supervision, raising the average LIBERO success rate from 79.0% to 92.5%, outperforming all same-backbone, same-critic baselines, and attaining high success rates on four real-robot manipulation tasks, including fine-grained plug insertion.

Training reinforcement learning (RL) agents on robotic tasks typically requires a large number of training samples. This is because training data often consists of noisy trajectories, whether from exploration or human-collected demonstrations, making it difficult to learn value functions that understand the effect of taking each action. On the other hand, recent behavior-cloning (BC) approaches have shown that predicting a sequence of actions enables policies to effectively approximate noisy, multi-modal distributions of expert demonstrations. Can we use a similar idea for improving RL on robotic tasks? In this paper, we introduce a novel RL algorithm that learns a critic network that outputs Q-values over a sequence of actions. By explicitly training the value functions to learn the consequence of executing a series of current and future actions, our algorithm allows for learning useful value functions from noisy trajectories. We study our algorithm across various setups with sparse and dense rewards, and with or without demonstrations, spanning mobile bi-manual manipulation, whole-body control, and tabletop manipulation tasks from BiGym, HumanoidBench, and RLBench. We find that, by learning the critic network with action sequences, our algorithm outperforms various RL and BC baselines, in particular on challenging humanoid control tasks.

Various test-time interventions for Computer Use Agents (CUAs), including critic models, have been developed to improve performance through pre-execution action evaluation in complex Graphical User Interface (GUI) environments. However, existing critics suffer from two key limitations: they (1) focus primarily on short-sighted decision loops (e.g., forgetting earlier actions) and (2) lack the visual grounding needed to detect flawed actions (e.g., clicking wrong UI elements). To address these, we introduce HiViG, a History-aware Visually Grounded test-time framework, built around a multimodal critic trained on real GUI trajectories to abstract past interactions into a compact record and to evaluate actions with visual grounding. At test time, HiViG integrates the critic into the policy decision loop to provide macro-action history, which summarizes the policy's completed achievements, and visually grounded critique, which verifies raw execution coordinates against the current screenshot to intercept errors before execution. Across web, mobile, and desktop benchmarks, HiViG consistently outperforms existing scalar and verbal critics, improving average success rates over the strongest baseline by 5.8% for Qwen3-VL-32B and 9.0% for Gemini-3-Flash, and demonstrates strong cross-platform generalization. Ablations show that macro-action history mitigates short-sighted planning and visually grounded critique reduces execution errors, with both components being critical for test-time scaling in long-horizon GUI tasks.

Flow-based generative models have shown remarkable success in text-to-image generation, yet fine-tuning them with intermediate feedback remains challenging, especially for continuous-time flow matching models. Most existing approaches solely learn from outcome rewards, struggling with the credit assignment problem. Alternative methods that attempt to learn a critic via direct regression on cumulative rewards often face training instabilities and model collapse in online settings. We present AC-Flow, a robust actor-critic framework that addresses these challenges through three key innovations: (1) reward shaping that provides well-normalized learning signals to enable stable intermediate value learning and gradient control, (2) a novel dual-stability mechanism that combines advantage clipping to prevent destructive policy updates with a warm-up phase that allows the critic to mature before influencing the actor, and (3) a scalable generalized critic weighting scheme that extends traditional reward-weighted methods while preserving model diversity through Wasserstein regularization. Through extensive experiments on Stable Diffusion 3, we demonstrate that AC-Flow achieves state-of-the-art performance in text-to-image alignment tasks and generalization to unseen human preference models. Our results demonstrate that even with a computationally efficient critic model, we can robustly finetune flow models without compromising generative quality, diversity, or stability.

Rejection Fine-Tuning (RFT) is a standard method for training LLM agents, where unsuccessful trajectories are discarded from the training set. In the context of SWE-bench tasks, this corresponds to filtering out runs where the submitted patch does not pass the tests. However, this approach discards unresolved trajectories, even though they form a large portion of all trajectories for hard tasks and even then may be partially correct. In this work, we propose Step Rejection Fine-Tuning (SRFT) - a practical way to leverage these unresolved trajectories. For this, we employ a critic LLM to assess the correctness of each step in a trajectory. Consequently, during training, we mask the loss for erroneous steps while retaining them in the context window. This way we ensure the model learns to recover from errors without reproducing them. Evaluation on SWE-bench Verified shows that while RFT improves the resolution rate by 2.4% by excluding unresolved trajectories, SRFT improves it by 3.7% by filtering them instead of discarding completely, reaching the total resolution rate of 32.2%.

Model-based reinforcement learning methods often use learning only for the purpose of estimating an approximate dynamics model, offloading the rest of the decision-making work to classical trajectory optimizers. While conceptually simple, this combination has a number of empirical shortcomings, suggesting that learned models may not be well-suited to standard trajectory optimization. In this paper, we consider what it would look like to fold as much of the trajectory optimization pipeline as possible into the modeling problem, such that sampling from the model and planning with it become nearly identical. The core of our technical approach lies in a diffusion probabilistic model that plans by iteratively denoising trajectories. We show how classifier-guided sampling and image inpainting can be reinterpreted as coherent planning strategies, explore the unusual and useful properties of diffusion-based planning methods, and demonstrate the effectiveness of our framework in control settings that emphasize long-horizon decision-making and test-time flexibility.

Instruction following is a fundamental ability of Large Language Models (LLMs), requiring their generated outputs to follow multiple constraints imposed in input instructions. Numerous studies have attempted to enhance this ability through preference optimization or reinforcement learning based on reward signals from LLM-as-a-Judge. However, existing evaluation models for instruction following still possess many deficiencies, such as substantial costs and unreliable assessments. To this end, we propose IF-CRITIC, an LLM critic that can provide efficient and reliable assessments of constraint following in the instructions. We first develop a checklist generator to decompose instructions and generate constraint checklists. With the assistance of the checklists, we collect high-quality critique training data through a multi-stage critique filtering mechanism and employ a constraint-level preference optimization method to train IF-CRITIC. Extensive experiments demonstrate that the evaluation performance of IF-CRITIC can beat strong LLM-as-a-Judge baselines, including Deepseek-R1 and o4-mini. With the scalable reward signals provided by IF-CRITIC, LLMs can achieve substantial performance gains in instruction-following optimization under lower computational overhead compared to strong LLM critic baselines.

Large Language Models (LLMs) have shown significant potential in designing reward functions for Reinforcement Learning (RL) tasks. However, obtaining high-quality reward code often involves human intervention, numerous LLM queries, or repetitive RL training. To address these issues, we propose CARD, a LLM-driven Reward Design framework that iteratively generates and improves reward function code. Specifically, CARD includes a Coder that generates and verifies the code, while a Evaluator provides dynamic feedback to guide the Coder in improving the code, eliminating the need for human feedback. In addition to process feedback and trajectory feedback, we introduce Trajectory Preference Evaluation (TPE), which evaluates the current reward function based on trajectory preferences. If the code fails the TPE, the Evaluator provides preference feedback, avoiding RL training at every iteration and making the reward function better aligned with the task objective. Empirical results on Meta-World and ManiSkill2 demonstrate that our method achieves an effective balance between task performance and token efficiency, outperforming or matching the baselines across all tasks. On 10 out of 12 tasks, CARD shows better or comparable performance to policies trained with expert-designed rewards, and our method even surpasses the oracle on 3 tasks.

This work investigates the reproducibility of the paper 'Explaining RL decisions with trajectories'. The original paper introduces a novel approach in explainable reinforcement learning based on the attribution decisions of an agent to specific clusters of trajectories encountered during training. We verify the main claims from the paper, which state that (i) training on less trajectories induces a lower initial state value, (ii) trajectories in a cluster present similar high-level patterns, (iii) distant trajectories influence the decision of an agent, and (iv) humans correctly identify the attributed trajectories to the decision of the agent. We recover the environments used by the authors based on the partial original code they provided for one of the environments (Grid-World), and implemented the remaining from scratch (Seaquest, HalfCheetah, Breakout and Q*Bert). While we confirm that (i), (ii), and (iii) partially hold, we extend on the largely qualitative experiments from the authors by introducing a quantitative metric to further support (iii), and new experiments and visual results for (i). Moreover, we investigate the use of different clustering algorithms and encoder architectures to further support (ii). We could not support (iv), given the limited extent of the original experiments. We conclude that, while some of the claims can be supported, further investigations and experiments could be of interest. We recognise the novelty of the work from the authors and hope that our work paves the way for clearer and more transparent approaches.

Multi-objective reinforcement learning for humanoid robots must coordinate locomotion and manipulation within a single policy. A natural design choice is whether to use a single (unified) critic that estimates the combined value of all objectives, or separate (dual) critics with disjoint reward signals. We present a controlled comparison on the Unitree G1 humanoid (23 active DoF) in NVIDIA Isaac Lab, training loco-manipulation policies through a sequential curriculum spanning 13 levels from stationary reaching to walking with variable-orientation targets. In standardized evaluation, dual-critic policies reach targets 3.5times faster (6.5 vs. 22.6 simulation steps), achieve 2times higher throughput (14.3 vs. 7.0 validated reaches per 1,000 steps), and attain higher validated reach rates (65.2% vs. 53.8%) compared to the unified-critic policy. Notably, additional anti-gaming reward mechanisms provide no further improvement beyond the architectural change alone (60.9% vs. 65.2%). These results have direct implications for the emerging paradigm of RL fine-tuning of imitation-learned policies: when refining a pre-trained manipulation policy with RL, a unified critic risks suppressing the learned behavior through competing locomotion gradients. These findings demonstrate that critic architecture is a primary - and often overlooked - design choice in multi-objective humanoid RL, with greater impact than reward engineering on reaching efficiency.

Agentic applications based on large language models increasingly rely on multi-step interaction loops involving planning, action execution, and environment feedback. While such systems are now deployed at scale, improving them post-deployment remains challenging. Agent trajectories are voluminous and non-deterministic, and reviewing each one, whether through human review or auxiliary LLMs, is slow and cost-prohibitive. We propose a lightweight, signal-based framework for triaging agentic interaction trajectories. Our approach computes cheap, broadly applicable signals from live interactions and attaches them as structured attributes for trajectory triage, identifying interactions likely to be informative without affecting online agent behavior. We organize signals into a coarse-grained taxonomy spanning interaction (misalignment, stagnation, disengagement, satisfaction), execution (failure, loop), and environment (exhaustion), designed for computation without model calls. In a controlled annotation study on τ-bench, a widely used benchmark for tool-augmented agent evaluation, we show that signal-based sampling achieves an 82\% informativeness rate compared to 74\% for heuristic filtering and 54\% for random sampling, with a 1.52x efficiency gain per informative trajectory. The advantage is robust across reward strata and task domains, confirming that signals provide genuine per-trajectory informativeness gains rather than merely oversampling obvious failures. These results show that lightweight signals can serve as practical sampling infrastructure for agentic systems, and suggest a path toward preference data construction and post-deployment optimization.

The average reward criterion is relatively less studied as most existing works in the Reinforcement Learning literature consider the discounted reward criterion. There are few recent works that present on-policy average reward actor-critic algorithms, but average reward off-policy actor-critic is relatively less explored. In this work, we present both on-policy and off-policy deterministic policy gradient theorems for the average reward performance criterion. Using these theorems, we also present an Average Reward Off-Policy Deep Deterministic Policy Gradient (ARO-DDPG) Algorithm. We first show asymptotic convergence analysis using the ODE-based method. Subsequently, we provide a finite time analysis of the resulting stochastic approximation scheme with linear function approximator and obtain an epsilon-optimal stationary policy with a sample complexity of Omega(epsilon^{-2.5}). We compare the average reward performance of our proposed ARO-DDPG algorithm and observe better empirical performance compared to state-of-the-art on-policy average reward actor-critic algorithms over MuJoCo-based environments.

Human motion generation is a critical task with a wide range of applications. Achieving high realism in generated motions requires naturalness, smoothness, and plausibility. Despite rapid advancements in the field, current generation methods often fall short of these goals. Furthermore, existing evaluation metrics typically rely on ground-truth-based errors, simple heuristics, or distribution distances, which do not align well with human perceptions of motion quality. In this work, we propose a data-driven approach to bridge this gap by introducing a large-scale human perceptual evaluation dataset, MotionPercept, and a human motion critic model, MotionCritic, that capture human perceptual preferences. Our critic model offers a more accurate metric for assessing motion quality and could be readily integrated into the motion generation pipeline to enhance generation quality. Extensive experiments demonstrate the effectiveness of our approach in both evaluating and improving the quality of generated human motions by aligning with human perceptions. Code and data are publicly available at https://motioncritic.github.io/.

The deployment of unmanned aerial vehicles (UAVs) for reliable and energy-efficient data collection from spatially distributed devices holds great promise in supporting diverse Internet of Things (IoT) applications. Nevertheless, the limited endurance and communication range of UAVs necessitate intelligent trajectory planning. While reinforcement learning (RL) has been extensively explored for UAV trajectory optimization, its interactive nature entails high costs and risks in real-world environments. Offline RL mitigates these issues but remains susceptible to unstable training and heavily rely on expert-quality datasets. To address these challenges, we formulate a joint UAV trajectory planning and resource allocation problem to maximize energy efficiency of data collection. The resource allocation subproblem is first transformed into an equivalent linear programming formulation and solved optimally with polynomial-time complexity. Then, we propose a large language model (LLM)-empowered critic-regularized decision transformer (DT) framework, termed LLM-CRDT, to learn effective UAV control policies. In LLM-CRDT, we incorporate critic networks to regularize the DT model training, thereby integrating the sequence modeling capabilities of DT with critic-based value guidance to enable learning effective policies from suboptimal datasets. Furthermore, to mitigate the data-hungry nature of transformer models, we employ a pre-trained LLM as the transformer backbone of the DT model and adopt a parameter-efficient fine-tuning strategy, i.e., LoRA, enabling rapid adaptation to UAV control tasks with small-scale dataset and low computational overhead. Extensive simulations demonstrate that LLM-CRDT outperforms benchmark online and offline RL methods, achieving up to 36.7\% higher energy efficiency than the current state-of-the-art DT approaches.

Proactive interventions by LLM critic models are often assumed to improve reliability, yet their effects at deployment time are poorly understood. We show that a binary LLM critic with strong offline accuracy (AUROC 0.94) can nevertheless cause severe performance degradation, inducing a 26 percentage point (pp) collapse on one model while affecting another by near zero pp. This variability demonstrates that LLM critic accuracy alone is insufficient to determine whether intervention is safe. We identify a disruption-recovery tradeoff: interventions may recover failing trajectories but also disrupt trajectories that would have succeeded. Based on this insight, we propose a pre-deployment test that uses a small pilot of 50 tasks to estimate whether intervention is likely to help or harm, without requiring full deployment. Across benchmarks, the test correctly anticipates outcomes: intervention degrades performance on high-success tasks (0 to -26 pp), while yielding a modest improvement on the high-failure ALFWorld benchmark (+2.8 pp, p=0.014). The primary value of our framework is therefore identifying when not to intervene, preventing severe regressions before deployment.

Trajectory-based data attribution methods estimate the influence of training samples on model predictions by unrolling the training trajectory. They are widely used in applications such as data selection, data valuation, and model diagnosis, but there is a lack of comprehensive error analysis of these methods, raising concerns about method faithfulness and hindering reliable deployment. In this work, we provide the first systematic analysis of error sources in trajectory-based data attribution, together with concrete remedies to mitigate them and practical guidelines for downstream use. We organize the total error into three categories, config-level, algorithm-level, and system-level. We make three contributions. First, we identify optimizer mismatch as the dominant config-level error: existing methods derive their attribution under the assumption of SGD, even for models trained with the modern de facto optimizer AdamW. We propose AdamW-influence to fully account for AdamW's optimization dynamics, yielding improvements from 10% to over 300% in Spearman correlation between estimated and ground-truth influence across four settings spanning MLP, CNN, GPT-2, and Llama 3.2-1B. Second, we isolate the remaining algorithm-level error arising from the first-order Taylor approximation, identify the learning rate and trajectory length as factors governing the error magnitude, and derive a closed-form error proxy that can be evaluated along the original trajectory without retraining. Third, we translate these insights into practical guidelines for data selection by unifying offline and online strategies under a K-step look-ahead framework. Under this framework, online selection with a short horizon often matches or exceeds offline, and the optimal horizon can be tuned jointly with the learning rate. Together, these results turn the framework into an actionable selection recipe for practitioners.

Policy-based methods currently dominate reinforcement learning (RL) pipelines for large language model (LLM) reasoning, leaving value-based approaches largely unexplored. We revisit the classical paradigm of Bellman Residual Minimization and introduce Trajectory Bellman Residual Minimization (TBRM), an algorithm that naturally adapts this idea to LLMs, yielding a simple yet effective off-policy algorithm that optimizes a single trajectory-level Bellman objective using the model's own logits as Q-values. TBRM removes the need for critics, importance-sampling ratios, or clipping, and operates with only one rollout per prompt. We prove convergence to the near-optimal KL-regularized policy from arbitrary off-policy data via an improved change-of-trajectory-measure analysis. Experiments on standard mathematical-reasoning benchmarks show that TBRM consistently outperforms policy-based baselines, like PPO and GRPO, with comparable or lower computational and memory overhead. Our results indicate that value-based RL might be a principled and efficient alternative for enhancing reasoning capabilities in LLMs.

Academic benchmarks for coding agents tend to reward autonomous task completion, measured by verifiable rewards such as unit-test success. In contrast, real-world coding agents operate with humans in the loop, where success signals are typically noisy, delayed, and sparse. How can we bridge this gap? In this paper, we propose a process to learn a "critic" model from sparse and noisy interaction data, which can then be used both as a reward model for either RL-based training or inference-time scaling. Specifically, we introduce Critic Rubrics, a rubric-based supervision framework with 24 behavioral features that can be derived from human-agent interaction traces alone. Using a semi-supervised objective, we can then jointly predict these rubrics and sparse human feedback (when present). In experiments, we demonstrate that, despite being trained primarily from trace-observable rubrics and sparse real-world outcome proxies, these critics improve best-of-N reranking on SWE-bench (Best@8 +15.9 over Random@8 over the rerankable subset of trajectories), enable early stopping (+17.7 with 83% fewer attempts), and support training-time data curation via critic-selected trajectories.

Robust pedestrian trajectory forecasting is crucial to developing safe autonomous vehicles. Although previous works have studied adversarial robustness in the context of trajectory forecasting, some significant issues remain unaddressed. In this work, we try to tackle these crucial problems. Firstly, the previous definitions of robustness in trajectory prediction are ambiguous. We thus provide formal definitions for two kinds of robustness, namely label robustness and pure robustness. Secondly, as previous works fail to consider robustness about all points in a disturbance interval, we utilise a probably approximately correct (PAC) framework for robustness verification. Additionally, this framework can not only identify potential counterexamples, but also provides interpretable analyses of the original methods. Our approach is applied using a prototype tool named TrajPAC. With TrajPAC, we evaluate the robustness of four state-of-the-art trajectory prediction models -- Trajectron++, MemoNet, AgentFormer, and MID -- on trajectories from five scenes of the ETH/UCY dataset and scenes of the Stanford Drone Dataset. Using our framework, we also experimentally study various factors that could influence robustness performance.

Group-based reinforcement learning methods such as GRPO for large language models avoid training a critic by sampling multiple responses for each prompt. A reliable critic could instead estimate token-level advantages from one response, but standard critic-based training recipes are often unstable. We study this instability and develop **Best Practice Critic Optimization (BPCO)**, a recipe that combines DPPO, value predictions bounded to the reward range, Monte Carlo value targets, unnormalized policy advantages, and length-adaptive generalized advantage estimation. Because the critic is used only during training, BPCO can also condition it on reward-defining information, such as a reference answer or grading rubric, that is hidden from the policy. Controlled experiments isolate the effect of each design choice. Across mathematical reasoning tasks with models ranging from 1.5B parameters to 30B-A3B mixtures of experts, BPCO improves a strong critic-based baseline consistently, and matches or exceeds a group-based baseline while sampling one response per prompt. The same recipe also improves learning with rubric-based rewards. These results show that a carefully designed critic provides a reliable alternative to group-relative advantage estimation. Code is available at https://github.com/QPHutu/golden_critic.

Group-relative methods for reinforcement learning with verifiable rewards (RLVR) learn from differences in rollout outcomes. Independently sampling complete trajectories is costly and does not explicitly explore the decision space at critical positions. Feedback on a completed trajectory can reveal which earlier choices the policy reconsiders, suggesting where to sample alternative continuations. We introduce Hindsight-Divergence Localization (HDL), which uses hindsight-induced changes in token log-likelihoods to select branch points. HDL generates a small number of complete root trajectories and fills each training group with continuations from the selected positions under the original task context. Each continuation reuses its root prefix and contributes policy updates only through its newly generated suffix, reducing generation cost while focusing additional exploration and learning on decisions after branching. Experiments with three models across math, code, and agent tasks show gains in both rollout efficiency and task performance. Compared with GRPO at matched group sizes and training steps, HDL yields up to a 2.5times reduction in generated tokens and a 1.8times speedup in rollout wall-clock time. Despite this reduced generation budget, HDL improves performance across all three domains, with gains of up to 12.5 points on agent tasks.

Reward modeling is crucial for aligning large language models (LLMs) with human preferences, especially in reinforcement learning from human feedback (RLHF). However, current reward models mainly produce scalar scores and struggle to incorporate critiques in a natural language format. We hypothesize that predicting both critiques and the scalar reward would improve reward modeling ability. Motivated by this, we propose Critic-RM, a framework that improves reward models using self-generated critiques without extra supervision. Critic-RM employs a two-stage process: generating and filtering high-quality critiques, followed by joint fine-tuning on reward prediction and critique generation. Experiments across benchmarks show that Critic-RM improves reward modeling accuracy by 3.7%-7.3% compared to standard reward models and LLM judges, demonstrating strong performance and data efficiency. Additional studies further validate the effectiveness of generated critiques in rectifying flawed reasoning steps with 2.5%-3.2% gains in improving reasoning accuracy.

Off-policy actor-critic methods in reinforcement learning train a critic with temporal-difference updates and use it as a learning signal for the policy (actor). This design typically achieves higher sample efficiency than purely on-policy methods. However, critic networks tend to overestimate value estimates systematically. This is often addressed by introducing a pessimistic bias based on uncertainty estimates. Current methods employ ensembling to quantify the critic's epistemic uncertainty-uncertainty due to limited data and model ambiguity-to scale pessimistic updates. In this work, we propose a new algorithm called Stochastic Actor-Critic (STAC) that incorporates temporal (one-step) aleatoric uncertainty-uncertainty arising from stochastic transitions, rewards, and policy-induced variability in Bellman targets-to scale pessimistic bias in temporal-difference updates, rather than relying on epistemic uncertainty. STAC uses a single distributional critic network to model the temporal return uncertainty, and applies dropout to both the critic and actor networks for regularization. Our results show that pessimism based on a distributional critic alone suffices to mitigate overestimation, and naturally leads to risk-averse behavior in stochastic environments. Introducing dropout further improves training stability and performance by means of regularization. With this design, STAC achieves improved computational efficiency using a single distributional critic network.

In this work, we address the challenging problem of long-horizon goal-reaching policy learning from non-expert, action-free observation data. Unlike fully labeled expert data, our data is more accessible and avoids the costly process of action labeling. Additionally, compared to online learning, which often involves aimless exploration, our data provides useful guidance for more efficient exploration. To achieve our goal, we propose a novel subgoal guidance learning strategy. The motivation behind this strategy is that long-horizon goals offer limited guidance for efficient exploration and accurate state transition. We develop a diffusion strategy-based high-level policy to generate reasonable subgoals as waypoints, preferring states that more easily lead to the final goal. Additionally, we learn state-goal value functions to encourage efficient subgoal reaching. These two components naturally integrate into the off-policy actor-critic framework, enabling efficient goal attainment through informative exploration. We evaluate our method on complex robotic navigation and manipulation tasks, demonstrating a significant performance advantage over existing methods. Our ablation study further shows that our method is robust to observation data with various corruptions.

Agentic search systems iteratively interact with retrieval models to answer complex queries. Despite substantial progress, optimizing retrievers for agentic search remains challenging, often requiring heavy co-training or gold-standard annotations that limit real-world applicability. We propose Critic-R, a framework that explicitly closes the feedback loop between the reasoning agent and the retrieval model during both inference and training. Critic-R introduces a critic model that evaluates the agent's introspective reasoning trace after consuming retrieved evidence to determine whether the retrieved context sufficiently supports the next reasoning step. Critic-R has two complementary mechanisms: Critic-R-Zero, an inference-time query refinement loop that iteratively rewrites queries and retrieval instructions, and Critic-Embed, an optimization approach for retrieval models that leverages successful and failed refinement trajectories as automatic supervision without requiring manual relevance annotation. We evaluate Critic-R on HotpotQA, 2WikiMultihopQA, MuSiQue, and Bamboogle. Results show that Critic-R significantly improves both retrieval quality and downstream answer accuracy.

Recent work has demonstrated the effectiveness of formulating decision making as a supervised learning problem on offline-collected trajectories. However, the benefits of performing sequence modeling on trajectory data is not yet clear. In this work we investigate if sequence modeling has the capability to condense trajectories into useful representations that can contribute to policy learning. To achieve this, we adopt a two-stage framework that first summarizes trajectories with sequence modeling techniques, and then employs these representations to learn a policy along with a desired goal. This design allows many existing supervised offline RL methods to be considered as specific instances of our framework. Within this framework, we introduce Goal-Conditioned Predicitve Coding (GCPC), an approach that brings powerful trajectory representations and leads to performant policies. We conduct extensive empirical evaluations on AntMaze, FrankaKitchen and Locomotion environments, and observe that sequence modeling has a significant impact on some decision making tasks. In addition, we demonstrate that GCPC learns a goal-conditioned latent representation about the future, which serves as an "implicit planner", and enables competitive performance on all three benchmarks.

Off-policy learning from multistep returns is crucial for sample-efficient reinforcement learning, but counteracting off-policy bias without exacerbating variance is challenging. Classically, off-policy bias is corrected in a per-decision manner: past temporal-difference errors are re-weighted by the instantaneous Importance Sampling (IS) ratio after each action via eligibility traces. Many off-policy algorithms rely on this mechanism, along with differing protocols for cutting the IS ratios to combat the variance of the IS estimator. Unfortunately, once a trace has been fully cut, the effect cannot be reversed. This has led to the development of credit-assignment strategies that account for multiple past experiences at a time. These trajectory-aware methods have not been extensively analyzed, and their theoretical justification remains uncertain. In this paper, we propose a multistep operator that can express both per-decision and trajectory-aware methods. We prove convergence conditions for our operator in the tabular setting, establishing the first guarantees for several existing methods as well as many new ones. Finally, we introduce Recency-Bounded Importance Sampling (RBIS), which leverages trajectory awareness to perform robustly across lambda-values in an off-policy control task.

We propose a conceptually simple and lightweight framework for deep reinforcement learning that uses asynchronous gradient descent for optimization of deep neural network controllers. We present asynchronous variants of four standard reinforcement learning algorithms and show that parallel actor-learners have a stabilizing effect on training allowing all four methods to successfully train neural network controllers. The best performing method, an asynchronous variant of actor-critic, surpasses the current state-of-the-art on the Atari domain while training for half the time on a single multi-core CPU instead of a GPU. Furthermore, we show that asynchronous actor-critic succeeds on a wide variety of continuous motor control problems as well as on a new task of navigating random 3D mazes using a visual input.

Existing Large Language Model (LLM) agents struggle in interactive environments requiring long-horizon planning, primarily due to compounding errors when simulating future states. To address this, we propose ProAct, a framework that enables agents to internalize accurate lookahead reasoning through a two-stage training paradigm. First, we introduce Grounded LookAhead Distillation (GLAD), where the agent undergoes supervised fine-tuning on trajectories derived from environment-based search. By compressing complex search trees into concise, causal reasoning chains, the agent learns the logic of foresight without the computational overhead of inference-time search. Second, to further refine decision accuracy, we propose the Monte-Carlo Critic (MC-Critic), a plug-and-play auxiliary value estimator designed to enhance policy-gradient algorithms like PPO and GRPO. By leveraging lightweight environment rollouts to calibrate value estimates, MC-Critic provides a low-variance signal that facilitates stable policy optimization without relying on expensive model-based value approximation. Experiments on both stochastic (e.g., 2048) and deterministic (e.g., Sokoban) environments demonstrate that ProAct significantly improves planning accuracy. Notably, a 4B parameter model trained with ProAct outperforms all open-source baselines and rivals state-of-the-art closed-source models, while demonstrating robust generalization to unseen environments. The codes and models are available at https://github.com/GreatX3/ProAct

Training critiquing language models to assess and provide feedback on model outputs is a promising way to improve LLMs for complex reasoning tasks. However, existing approaches typically rely on stronger supervisors for annotating critique data. To address this, we propose Critique-RL, an online RL approach for developing critiquing language models without stronger supervision. Our approach operates on a two-player paradigm: the actor generates a response, the critic provides feedback, and the actor refines the response accordingly. We first reveal that relying solely on indirect reward signals from the actor's outputs for RL optimization often leads to unsatisfactory critics: while their helpfulness (i.e., providing constructive feedback) improves, the discriminability (i.e., determining whether a response is high-quality or not) remains poor, resulting in marginal performance gains. To overcome this, Critique-RL adopts a two-stage optimization strategy. In stage I, it reinforces the discriminability of the critic with direct rule-based reward signals; in stage II, it introduces indirect rewards based on actor refinement to improve the critic's helpfulness, while maintaining its discriminability via appropriate regularization. Extensive experiments across various tasks and models show that Critique-RL delivers substantial performance improvements. For example, it achieves a 9.02% gain on in-domain tasks and a 5.70% gain on out-of-domain tasks for Qwen2.5-7B, highlighting its potential.

Reward design remains a central bottleneck for autonomous robot policy improvement, especially in long-horizon manipulation tasks where sparse success labels provide too little signal and binary preferences collapse many competing notions of quality into one ambiguous signal. We introduce Freeform Preference Learning (FPL), a method for learning robot policies from freeform human preferences. Rather than asking annotators which of two trajectories is better overall, FPL lets them define natural-language preference axes, such as speed, safety, quality of placement, or carefulness, and provide pairwise preferences along each axis. These annotations are used to learn a language-conditioned reward model that maps a trajectory and preference label to an axis-specific reward. We use this model to train a reward-conditioned policy that optimizes across the multiple human-specified dimensions. Across four real-world and two simulated long-horizon manipulation tasks, FPL improves over sparse-reward and binary-preference methods by 38 percentage points. Beyond improved performance, FPL learns dense progress signals without explicit subtask segmentation, shows compositionality of behavior not present in the data, and allows users to steer the policy towards different behaviors at test time without retraining. Blog post with videos available at https://freeform-pl.github.io/fpl.website/

The Reinforcement Learning (RL) building blocks, i.e. Q-functions and policy networks, usually take elements from the cartesian product of two domains as input. In particular, the input of the Q-function is both the state and the action, and in multi-task problems (Meta-RL) the policy can take a state and a context. Standard architectures tend to ignore these variables' underlying interpretations and simply concatenate their features into a single vector. In this work, we argue that this choice may lead to poor gradient estimation in actor-critic algorithms and high variance learning steps in Meta-RL algorithms. To consider the interaction between the input variables, we suggest using a Hypernetwork architecture where a primary network determines the weights of a conditional dynamic network. We show that this approach improves the gradient approximation and reduces the learning step variance, which both accelerates learning and improves the final performance. We demonstrate a consistent improvement across different locomotion tasks and different algorithms both in RL (TD3 and SAC) and in Meta-RL (MAML and PEARL).

Offline reinforcement learning faces a significant challenge of value over-estimation due to the distributional drift between the dataset and the current learned policy, leading to learning failure in practice. The common approach is to incorporate a penalty term to reward or value estimation in the Bellman iterations. Meanwhile, to avoid extrapolation on out-of-distribution (OOD) states and actions, existing methods focus on conservative Q-function estimation. In this paper, we propose Conservative State Value Estimation (CSVE), a new approach that learns conservative V-function via directly imposing penalty on OOD states. Compared to prior work, CSVE allows more effective in-data policy optimization with conservative value guarantees. Further, we apply CSVE and develop a practical actor-critic algorithm in which the critic does the conservative value estimation by additionally sampling and penalizing the states around the dataset, and the actor applies advantage weighted updates extended with state exploration to improve the policy. We evaluate in classic continual control tasks of D4RL, showing that our method performs better than the conservative Q-function learning methods and is strongly competitive among recent SOTA methods.

Large Language Models (LLMs) have become integral components in various autonomous agent systems. In this study, we present an exploration-based trajectory optimization approach, referred to as ETO. This learning method is designed to enhance the performance of open LLM agents. Contrary to previous studies that exclusively train on successful expert trajectories, our method allows agents to learn from their exploration failures. This leads to improved performance through an iterative optimization framework. During the exploration phase, the agent interacts with the environment while completing given tasks, gathering failure trajectories to create contrastive trajectory pairs. In the subsequent training phase, the agent utilizes these trajectory preference pairs to update its policy using contrastive learning methods like DPO. This iterative cycle of exploration and training fosters continued improvement in the agents. Our experiments on three complex tasks demonstrate that ETO consistently surpasses baseline performance by a large margin. Furthermore, an examination of task-solving efficiency and potential in scenarios lacking expert trajectory underscores the effectiveness of our approach.

In classical Reinforcement Learning from Human Feedback (RLHF), Reward Models (RMs) serve as the fundamental signal provider for model alignment. As Large Language Models evolve into agentic systems capable of autonomous tool invocation and complex reasoning, the paradigm of reward modeling faces unprecedented challenges--most notably, the lack of benchmarks specifically designed to assess RM capabilities within tool-integrated environments. To address this gap, we present Plan-RewardBench, a trajectory-level preference benchmark designed to evaluate how well judges distinguish preferred versus distractor agent trajectories in complex tool-using scenarios. Plan-RewardBench covers four representative task families -- (i) Safety Refusal, (ii) Tool-Irrelevance / Unavailability, (iii) Complex Planning, and (iv) Robust Error Recovery -- comprising validated positive trajectories and confusable hard negatives constructed via multi-model natural rollouts, rule-based perturbations, and minimal-edit LLM perturbations. We benchmark representative RMs (generative, discriminative, and LLM-as-Judge) under a unified pairwise protocol, reporting accuracy trends across varying trajectory lengths and task categories. Furthermore, we provide diagnostic analyses of prevalent failure modes. Our results reveal that all three evaluator families face substantial challenges, with performance degrading sharply on long-horizon trajectories, underscoring the necessity for specialized training in agentic, trajectory-level reward modeling. Ultimately, Plan-RewardBench aims to serve as both a practical evaluation suite and a reusable blueprint for constructing agentic planning preference data.

We consider the problem of designing a smooth trajectory that traverses a sequence of convex sets in minimum time, while satisfying given velocity and acceleration constraints. This problem is naturally formulated as a nonconvex program. To solve it, we propose a biconvex method that quickly produces an initial trajectory and iteratively refines it by solving two convex subproblems in alternation. This method is guaranteed to converge, returns a feasible trajectory even if stopped early, and does not require the selection of any line-search or trust-region parameter. Exhaustive experiments show that our method finds high-quality trajectories in a fraction of the time of state-of-the-art solvers for nonconvex optimization. In addition, it achieves runtimes comparable to industry-standard waypoint-based motion planners, while consistently designing lower-duration trajectories than existing optimization-based planners.

This paper investigates the problem of interactively learning behaviors communicated by a human teacher using positive and negative feedback. Much previous work on this problem has made the assumption that people provide feedback for decisions that is dependent on the behavior they are teaching and is independent from the learner's current policy. We present empirical results that show this assumption to be false -- whether human trainers give a positive or negative feedback for a decision is influenced by the learner's current policy. Based on this insight, we introduce {\em Convergent Actor-Critic by Humans} (COACH), an algorithm for learning from policy-dependent feedback that converges to a local optimum. Finally, we demonstrate that COACH can successfully learn multiple behaviors on a physical robot.

Natural-language critiques provide supervision beyond scalar rewards for non-verifiable generation, which lacks deterministic verifiers. In critique-guided refinement, a critic gives feedback on an initial response and an actor revises it. However, final revision quality does not reveal whether the critique was actually useful: a capable actor may improve without following the feedback, while valid feedback may fail if the actor cannot execute it. We frame critique as actor-conditioned revision guidance, where usefulness depends on whether the feedback helps the target actor address the intended weakness. We introduce TAIScore (Targeted Actionable Improvement Score), a reward that evaluates the instruction, initial response, critique, and revision together, assessing whether the critique targets a real weakness, whether the actor follows it, and whether the intended aspect improves. We use this reward to train an actor-tailored critic with GRPO, and use critique-guided refinements to construct DPO preference pairs for the actor, forming a co-evolving critic-actor loop where the critic adapts to the actor's changing capability. Experiments show that an 8B critic trained with TAIScore outperforms both a zero-shot 120B critic and critics trained with outcome-only or critique-only reward signals. Co-evolving the critic and actor further improves performance, suggesting that effective critique supervision should adapt as the actor changes.

Recent developments in large language models (LLMs) have been impressive. However, these models sometimes show inconsistencies and problematic behavior, such as hallucinating facts, generating flawed code, or creating offensive and toxic content. Unlike these models, humans typically utilize external tools to cross-check and refine their initial content, like using a search engine for fact-checking, or a code interpreter for debugging. Inspired by this observation, we introduce a framework called CRITIC that allows LLMs, which are essentially "black boxes" to validate and progressively amend their own outputs in a manner similar to human interaction with tools. More specifically, starting with an initial output, CRITIC interacts with appropriate tools to evaluate certain aspects of the text, and then revises the output based on the feedback obtained during this validation process. Comprehensive evaluations involving free-form question answering, mathematical program synthesis, and toxicity reduction demonstrate that CRITIC consistently enhances the performance of LLMs. Meanwhile, our research highlights the crucial importance of external feedback in promoting the ongoing self-improvement of LLMs.

In cognitive science, resource rationality asks how an agent should allocate limited computation to maximize expected value. Most reasoning and agent benchmarks use independent per-task budgets; existing shared-budget studies do not calibrate suite performance against the same model's demonstrated single-problem competence. We introduce R^3-Bench, which evaluates six-problem suites under shared budgets across mathematics, competitive programming, and abstract reasoning in tool-free and agentic settings. Matched single-problem response curves define an offline empirical oracle over observed successes. Across 72 main-table cells for six models, the oracle mean matches or exceeds the contest mean in all cells and is strictly higher in 71. Under moderate tool-free pressure, equal-allocation replay also exceeds contest performance for four of six models. Trajectory diagnostics reveal limited strategy updating and pressure-dependent failure patterns. In a three-model diagnostic under strong agentic pressure, at least one fixed scheduler exceeds the contest mean in six of nine cells, but no policy dominates across domains. These results expose a persistent gap between demonstrated competence and shared-budget realization.

Recent work shows that flow matching can be effective for scalar Q-value function estimation in reinforcement learning (RL), but it remains unclear why or how this approach differs from standard critics. Contrary to conventional belief, we show that their success is not explained by distributional RL, as explicitly modeling return distributions can reduce performance. Instead, we argue that the use of integration for reading out values and dense velocity supervision at each step of this integration process for training improves TD learning via two mechanisms. First, it enables robust value prediction through test-time recovery, whereby iterative computation through integration dampens errors in early value estimates as more integration steps are performed. This recovery mechanism is absent in monolithic critics. Second, supervising the velocity field at multiple interpolant values induces more plastic feature learning within the network, allowing critics to represent non-stationary TD targets without discarding previously learned features or overfitting to individual TD targets encountered during training. We formalize these effects and validate them empirically, showing that flow-matching critics substantially outperform monolithic critics (2times in final performance and around 5times in sample efficiency) in settings where loss of plasticity poses a challenge e.g., in high-UTD online RL problems, while remaining stable during learning.

Reinforcement learning (RL) can align language models with non-differentiable reward signals, such as human preferences. However, a major challenge arises from the sparsity of these reward signals - typically, there is only one reward for the entire generation. This sparsity of rewards can lead to inefficient and unstable learning. In this paper, we introduce a novel framework leveraging the critique ability of LLMs to produce dense rewards throughout the learning process. Our approach incorporates a critic language model alongside the policy model. This critic is prompted with the task description, question, policy model's output, and environment's reward signal as input, and provides token or span-level dense rewards that reflect the quality of each segment of the output. We assess our approach on three text generation tasks: sentiment control, language model detoxification, and summarization. Experimental results show that incorporating artificial dense rewards in training yields consistent performance gains over the PPO baseline with holistic rewards. Furthermore, in a setting where the same model serves as both policy and critic, we demonstrate that "self-critique" rewards also boost learning efficiency.

We propose a novel independent and payoff-based learning framework for stochastic games that is model-free, game-agnostic, and gradient-free. The learning dynamics follow a best-response-type actor-critic architecture, where agents update their strategies (actors) using feedback from two distinct critics: a fast critic that intuitively responds to observed payoffs under limited information, and a slow critic that deliberatively approximates the solution to the underlying dynamic programming problem. Crucially, the learning process relies on non-equilibrium adaptation through smoothed best responses to observed payoffs. We establish convergence to (approximate) equilibria in two-agent zero-sum and multi-agent identical-interest stochastic games over an infinite horizon. This provides one of the first payoff-based and fully decentralized learning algorithms with theoretical guarantees in both settings. Empirical results further validate the robustness and effectiveness of the proposed approach across both classes of games.

Large Language Models (LLMs) agents are increasingly pivotal for addressing complex tasks in interactive environments. Existing work mainly focuses on enhancing performance through behavior cloning from stronger experts, yet such approaches often falter in real-world applications, mainly due to the inability to recover from errors. However, step-level critique data is difficult and expensive to collect. Automating and dynamically constructing self-critique datasets is thus crucial to empowering models with intelligent agent capabilities. In this work, we propose an iterative self-training framework, Agent-R, that enables language Agent to Reflect on the fly. Unlike traditional methods that reward or penalize actions based on correctness, Agent-R leverages MCTS to construct training data that recover correct trajectories from erroneous ones. A key challenge of agent reflection lies in the necessity for timely revision rather than waiting until the end of a rollout. To address this, we introduce a model-guided critique construction mechanism: the actor model identifies the first error step (within its current capability) in a failed trajectory. Starting from it, we splice it with the adjacent correct path, which shares the same parent node in the tree. This strategy enables the model to learn reflection based on its current policy, therefore yielding better learning efficiency. To further explore the scalability of this self-improvement paradigm, we investigate iterative refinement of both error correction capabilities and dataset construction. Our findings demonstrate that Agent-R continuously improves the model's ability to recover from errors and enables timely error correction. Experiments on three interactive environments show that Agent-R effectively equips agents to correct erroneous actions while avoiding loops, achieving superior performance compared to baseline methods (+5.59%).

Sample efficiency and exploration remain major challenges in online reinforcement learning (RL). A powerful approach that can be applied to address these issues is the inclusion of offline data, such as prior trajectories from a human expert or a sub-optimal exploration policy. Previous methods have relied on extensive modifications and additional complexity to ensure the effective use of this data. Instead, we ask: can we simply apply existing off-policy methods to leverage offline data when learning online? In this work, we demonstrate that the answer is yes; however, a set of minimal but important changes to existing off-policy RL algorithms are required to achieve reliable performance. We extensively ablate these design choices, demonstrating the key factors that most affect performance, and arrive at a set of recommendations that practitioners can readily apply, whether their data comprise a small number of expert demonstrations or large volumes of sub-optimal trajectories. We see that correct application of these simple recommendations can provide a 2.5times improvement over existing approaches across a diverse set of competitive benchmarks, with no additional computational overhead. We have released our code at https://github.com/ikostrikov/rlpd.

We study an emerging problem named "grasping the invisible" in robotic manipulation, in which a robot is tasked to grasp an initially invisible target object via a sequence of pushing and grasping actions. In this problem, pushes are needed to search for the target and rearrange cluttered objects around it to enable effective grasps. We propose to solve the problem by formulating a deep learning approach in a critic-policy format. The target-oriented motion critic, which maps both visual observations and target information to the expected future rewards of pushing and grasping motion primitives, is learned via deep Q-learning. We divide the problem into two subtasks, and two policies are proposed to tackle each of them, by combining the critic predictions and relevant domain knowledge. A Bayesian-based policy accounting for past action experience performs pushing to search for the target; once the target is found, a classifier-based policy coordinates target-oriented pushing and grasping to grasp the target in clutter. The motion critic and the classifier are trained in a self-supervised manner through robot-environment interactions. Our system achieves a 93% and 87% task success rate on each of the two subtasks in simulation and an 85% task success rate in real robot experiments on the whole problem, which outperforms several baselines by large margins. Supplementary material is available at https://sites.google.com/umn.edu/grasping-invisible.

Most offline reinforcement learning (RL) algorithms return a target policy maximizing a trade-off between (1) the expected performance gain over the behavior policy that collected the dataset, and (2) the risk stemming from the out-of-distribution-ness of the induced state-action occupancy. It follows that the performance of the target policy is strongly related to the performance of the behavior policy and, thus, the trajectory return distribution of the dataset. We show that in mixed datasets consisting of mostly low-return trajectories and minor high-return trajectories, state-of-the-art offline RL algorithms are overly restrained by low-return trajectories and fail to exploit high-performing trajectories to the fullest. To overcome this issue, we show that, in deterministic MDPs with stochastic initial states, the dataset sampling can be re-weighted to induce an artificial dataset whose behavior policy has a higher return. This re-weighted sampling strategy may be combined with any offline RL algorithm. We further analyze that the opportunity for performance improvement over the behavior policy correlates with the positive-sided variance of the returns of the trajectories in the dataset. We empirically show that while CQL, IQL, and TD3+BC achieve only a part of this potential policy improvement, these same algorithms combined with our reweighted sampling strategy fully exploit the dataset. Furthermore, we empirically demonstrate that, despite its theoretical limitation, the approach may still be efficient in stochastic environments. The code is available at https://github.com/Improbable-AI/harness-offline-rl.

Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to sampling-based planners that struggle in very high dimensions and with continuous differential constraints. Indeed, obstacles are the source of many textbook examples of problematic nonconvexities in the trajectory-optimization problem. Here we show that convex optimization can, in fact, be used to reliably plan trajectories around obstacles. Specifically, we consider planning problems with collision-avoidance constraints, as well as cost penalties and hard constraints on the shape, the duration, and the velocity of the trajectory. Combining the properties of Bézier curves with a recently-proposed framework for finding shortest paths in Graphs of Convex Sets (GCS), we formulate the planning problem as a compact mixed-integer optimization. In stark contrast with existing mixed-integer planners, the convex relaxation of our programs is very tight, and a cheap rounding of its solution is typically sufficient to design globally-optimal trajectories. This reduces the mixed-integer program back to a simple convex optimization, and automatically provides optimality bounds for the planned trajectories. We name the proposed planner GCS, after its underlying optimization framework. We demonstrate GCS in simulation on a variety of robotic platforms, including a quadrotor flying through buildings and a dual-arm manipulator (with fourteen degrees of freedom) moving in a confined space. Using numerical experiments on a seven-degree-of-freedom manipulator, we show that GCS can outperform widely-used sampling-based planners by finding higher-quality trajectories in less time.

We consider an improper reinforcement learning setting where a learner is given M base controllers for an unknown Markov decision process, and wishes to combine them optimally to produce a potentially new controller that can outperform each of the base ones. This can be useful in tuning across controllers, learnt possibly in mismatched or simulated environments, to obtain a good controller for a given target environment with relatively few trials. Towards this, we propose two algorithms: (1) a Policy Gradient-based approach; and (2) an algorithm that can switch between a simple Actor-Critic (AC) based scheme and a Natural Actor-Critic (NAC) scheme depending on the available information. Both algorithms operate over a class of improper mixtures of the given controllers. For the first case, we derive convergence rate guarantees assuming access to a gradient oracle. For the AC-based approach we provide convergence rate guarantees to a stationary point in the basic AC case and to a global optimum in the NAC case. Numerical results on (i) the standard control theoretic benchmark of stabilizing an cartpole; and (ii) a constrained queueing task show that our improper policy optimization algorithm can stabilize the system even when the base policies at its disposal are unstable.

As agentic systems tackle increasingly complex multi-step tasks, evaluating their trajectories presents a major bottleneck - human annotation of a single trajectory on popular agentic benchmarks can take hours, making it difficult to scale evaluations for measuring performance or curating training data. This has driven widespread reliance on automated approaches such as LLM-as-a-judge (LLMJ) to critique agents at the process and outcome-levels at scale, however, the soundness of LLMJ critiques often goes unmeasured. Here, we introduce Counsel, the first public dataset of meta-evaluations for agentic tasks. Counsel consists of process-level critiques from open-weight LLMJs on two agent benchmarks: tau-bench (customer support agents) and DA-Code (coding agents), and human meta-evaluations of these critiques. Human annotators label critiques on each flagged error as "spot on", "correct location but poor reasoning", or "should not have flagged", achieving reliable inter-annotator agreement (Krippendorff's alpha of 0.78). The resulting dataset stratifies LLMJ critiques by human alignment across both error location within a trajectory and reasoning quality, serving as valuable data to calibrate, improve, or train LLMJs for agents. Comparing open-weight judges, we find that more capable judge models and more reasoning effort both enabled improved human agreement, with the strongest judge reaching ~88% agreement on location and ~65% on reasoning. Counsel is generated using open-weight models and is permissively licensed for broad community use, which we hope will enable rigorous study and improved alignment of LLM-based evaluators for agentic systems.

We introduce the framework of performative reinforcement learning where the policy chosen by the learner affects the underlying reward and transition dynamics of the environment. Following the recent literature on performative prediction~Perdomo et. al., 2020, we introduce the concept of performatively stable policy. We then consider a regularized version of the reinforcement learning problem and show that repeatedly optimizing this objective converges to a performatively stable policy under reasonable assumptions on the transition dynamics. Our proof utilizes the dual perspective of the reinforcement learning problem and may be of independent interest in analyzing the convergence of other algorithms with decision-dependent environments. We then extend our results for the setting where the learner just performs gradient ascent steps instead of fully optimizing the objective, and for the setting where the learner has access to a finite number of trajectories from the changed environment. For both settings, we leverage the dual formulation of performative reinforcement learning and establish convergence to a stable solution. Finally, through extensive experiments on a grid-world environment, we demonstrate the dependence of convergence on various parameters e.g. regularization, smoothness, and the number of samples.

Reinforcement learning with verifiable rewards has become a central tool for improving the reasoning ability of large language models, but current methods face a trade-off between simplicity and credit assignment. Group-relative methods such as GRPO avoid training a critic, but typically assign a trajectory-level advantage to every token. Actor-critic methods provide denser learning signals, but require a learned value function with its own training instability. We introduce VIMPO, a critic-free policy optimization method that derives a policy-implied value function from the optimality conditions of KL-regularized reinforcement learning. For autoregressive generation, the resulting value recurrence can be written in terms of policy-reference log-ratios and anchored by the terminal condition that no future reward remains at the end of a trajectory. This gives a simple value loss that incorporates outcome-level verifiable rewards without training a critic. The same derivation also yields a critic-free actor advantage, allowing VIMPO to separate reward incorporation through the value loss from policy improvement through a PPO-style actor update. On mathematical RLVR benchmarks, VIMPO improves over GRPO across MATH-500, AIME 2024, AIME 2025, and OlympiadBench, with especially larger gains on competition-style evaluations. Under noisy rewards, VIMPO retains a consistent advantage over GRPO, suggesting that policy-implied value optimization can provide finer credit assignment while preserving the practical simplicity of critic-free training.

Grounding the reasoning ability of large language models (LLMs) for embodied tasks is challenging due to the complexity of the physical world. Especially, LLM planning for multi-agent collaboration requires communication of agents or credit assignment as the feedback to re-adjust the proposed plans and achieve effective coordination. However, existing methods that overly rely on physical verification or self-reflection suffer from excessive and inefficient querying of LLMs. In this paper, we propose a novel framework for multi-agent collaboration that introduces Reinforced Advantage feedback (ReAd) for efficient self-refinement of plans. Specifically, we perform critic regression to learn a sequential advantage function from LLM-planned data, and then treat the LLM planner as an optimizer to generate actions that maximize the advantage function. It endows the LLM with the foresight to discern whether the action contributes to accomplishing the final task. We provide theoretical analysis by extending advantage-weighted regression in reinforcement learning to multi-agent systems. Experiments on Overcooked-AI and a difficult variant of RoCoBench show that ReAd surpasses baselines in success rate, and also significantly decreases the interaction steps of agents and query rounds of LLMs, demonstrating its high efficiency for grounding LLMs. More results are given at https://read-llm.github.io/.

Teaching large language models (LLMs) to critique and refine their outputs is crucial for building systems that can iteratively improve, yet it is fundamentally limited by the ability to provide accurate judgments and actionable suggestions. In this work, we study LLM critics for code generation and propose CTRL, a framework for Critic Training via Reinforcement Learning, which trains a critic model to generate feedback that maximizes correction performance for a fixed generator model without human supervision. Our results demonstrate that critics trained with CTRL significantly enhance pass rates and mitigate compounding errors across both base and stronger generator models. Furthermore, we show that these critic models act as accurate generative reward models and enable test-time scaling through iterative critique-revision, achieving up to 106.1% relative improvements across challenging code generation benchmarks.

Policy gradient methods rely on a baseline to measure the relative advantage of an action, ensuring the model reinforces behaviors that outperform its current average capability. In the training of Large Language Models (LLMs) using Actor-Critic methods (e.g., PPO), this baseline is typically estimated by a Value Model (Critic) often as large as the policy model itself. However, as the policy continuously evolves, the value model requires expensive, synchronous incremental training to accurately track the shifting capabilities of the policy. To avoid this overhead, Group Relative Policy Optimization (GRPO) eliminates the coupled value model by using the average reward of a group of rollouts as the baseline; yet, this approach necessitates extensive sampling to maintain estimation stability. In this paper, we propose V_0, a Generalist Value Model capable of estimating the expected performance of any model on unseen prompts without requiring parameter updates. We reframe value estimation by treating the policy's dynamic capability as an explicit context input; specifically, we leverage a history of instruction-performance pairs to dynamically profile the model, departing from the traditional paradigm that relies on parameter fitting to perceive capability shifts. Focusing on value estimation at State Zero (i.e., the initial prompt, hence V_0), our model serves as a critical resource scheduler. During GRPO training, V_0 predicts success rates prior to rollout, allowing for efficient sampling budget allocation; during deployment, it functions as a router, dispatching instructions to the most cost-effective and suitable model. Empirical results demonstrate that V_0 significantly outperforms heuristic budget allocation and achieves a Pareto-optimal trade-off between performance and cost in LLM routing tasks.

Offline preference-based reinforcement learning (PbRL) typically operates in two phases: first, use human preferences to learn a reward model and annotate rewards for a reward-free offline dataset; second, learn a policy by optimizing the learned reward via offline RL. However, accurately modeling step-wise rewards from trajectory-level preference feedback presents inherent challenges. The reward bias introduced, particularly the overestimation of predicted rewards, leads to optimistic trajectory stitching, which undermines the pessimism mechanism critical to the offline RL phase. To address this challenge, we propose In-Dataset Trajectory Return Regularization (DTR) for offline PbRL, which leverages conditional sequence modeling to mitigate the risk of learning inaccurate trajectory stitching under reward bias. Specifically, DTR employs Decision Transformer and TD-Learning to strike a balance between maintaining fidelity to the behavior policy with high in-dataset trajectory returns and selecting optimal actions based on high reward labels. Additionally, we introduce an ensemble normalization technique that effectively integrates multiple reward models, balancing the tradeoff between reward differentiation and accuracy. Empirical evaluations on various benchmarks demonstrate the superiority of DTR over other state-of-the-art baselines.

Many reinforcement learning environments (e.g., Minecraft) provide only sparse rewards that indicate task completion or failure with binary values. The challenge in exploration efficiency in such environments makes it difficult for reinforcement-learning-based agents to learn complex tasks. To address this, this paper introduces an advanced learning system, named Auto MC-Reward, that leverages Large Language Models (LLMs) to automatically design dense reward functions, thereby enhancing the learning efficiency. Auto MC-Reward consists of three important components: Reward Designer, Reward Critic, and Trajectory Analyzer. Given the environment information and task descriptions, the Reward Designer first design the reward function by coding an executable Python function with predefined observation inputs. Then, our Reward Critic will be responsible for verifying the code, checking whether the code is self-consistent and free of syntax and semantic errors. Further, the Trajectory Analyzer summarizes possible failure causes and provides refinement suggestions according to collected trajectories. In the next round, Reward Designer will further refine and iterate the dense reward function based on feedback. Experiments demonstrate a significant improvement in the success rate and learning efficiency of our agents in complex tasks in Minecraft, such as obtaining diamond with the efficient ability to avoid lava, and efficiently explore trees and animals that are sparse in the plains biome.

For continuous action spaces, actor-critic methods are widely used in online reinforcement learning (RL). However, unlike RL algorithms for discrete actions, which generally model the optimal value function using the Bellman optimality operator, RL algorithms for continuous actions typically model Q-values for the current policy using the Bellman operator. These algorithms for continuous actions rely exclusively on policy updates for improvement, which often results in low sample efficiency. This study examines the effectiveness of incorporating the Bellman optimality operator into actor-critic frameworks. Experiments in a simple environment show that modeling optimal values accelerates learning but leads to overestimation bias. To address this, we propose an annealing approach that gradually transitions from the Bellman optimality operator to the Bellman operator, thereby accelerating learning while mitigating bias. Our method, combined with TD3 and SAC, significantly outperforms existing approaches across various locomotion and manipulation tasks, demonstrating improved performance and robustness to hyperparameters related to optimality. The code for this study is available at https://github.com/motokiomura/annealed-q-learning.

We propose a reinforcement learning (RL) framework under a broad class of risk objectives, characterized by convex scoring functions. This class covers many common risk measures, such as variance, Expected Shortfall, entropic Value-at-Risk, and mean-risk utility. To resolve the time-inconsistency issue, we consider an augmented state space and an auxiliary variable and recast the problem as a two-state optimization problem. We propose a customized Actor-Critic algorithm and establish some theoretical approximation guarantees. A key theoretical contribution is that our results do not require the Markov decision process to be continuous. Additionally, we propose an auxiliary variable sampling method inspired by the alternating minimization algorithm, which is convergent under certain conditions. We validate our approach in simulation experiments with a financial application in statistical arbitrage trading, demonstrating the effectiveness of the algorithm.

We study a new paradigm for sequential decision making, called offline Policy Learning from Observation (PLfO). Offline PLfO aims to learn policies using datasets with substandard qualities: 1) only a subset of trajectories is labeled with rewards, 2) labeled trajectories may not contain actions, 3) labeled trajectories may not be of high quality, and 4) the overall data may not have full coverage. Such imperfection is common in real-world learning scenarios, so offline PLfO encompasses many existing offline learning setups, including offline imitation learning (IL), ILfO, and reinforcement learning (RL). In this work, we present a generic approach, called Modality-agnostic Adversarial Hypothesis Adaptation for Learning from Observations (MAHALO), for offline PLfO. Built upon the pessimism concept in offline RL, MAHALO optimizes the policy using a performance lower bound that accounts for uncertainty due to the dataset's insufficient converge. We implement this idea by adversarially training data-consistent critic and reward functions in policy optimization, which forces the learned policy to be robust to the data deficiency. We show that MAHALO consistently outperforms or matches specialized algorithms across a variety of offline PLfO tasks in theory and experiments.

Multi-modal trajectory forecasting methods commonly evaluate using single-agent metrics (marginal metrics), such as minimum Average Displacement Error (ADE) and Final Displacement Error (FDE), which fail to capture joint performance of multiple interacting agents. Only focusing on marginal metrics can lead to unnatural predictions, such as colliding trajectories or diverging trajectories for people who are clearly walking together as a group. Consequently, methods optimized for marginal metrics lead to overly-optimistic estimations of performance, which is detrimental to progress in trajectory forecasting research. In response to the limitations of marginal metrics, we present the first comprehensive evaluation of state-of-the-art (SOTA) trajectory forecasting methods with respect to multi-agent metrics (joint metrics): JADE, JFDE, and collision rate. We demonstrate the importance of joint metrics as opposed to marginal metrics with quantitative evidence and qualitative examples drawn from the ETH / UCY and Stanford Drone datasets. We introduce a new loss function incorporating joint metrics that, when applied to a SOTA trajectory forecasting method, achieves a 7% improvement in JADE / JFDE on the ETH / UCY datasets with respect to the previous SOTA. Our results also indicate that optimizing for joint metrics naturally leads to an improvement in interaction modeling, as evidenced by a 16% decrease in mean collision rate on the ETH / UCY datasets with respect to the previous SOTA.

A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e.g.~iLQR - on the learned model to minimize a target cost. This paper conducts a rigorous analysis of a simplified variant of this strategy for general nonlinear systems. We analyze an algorithm which iterates between estimating local linear models of nonlinear system dynamics and performing iLQR-like policy updates. We demonstrate that this algorithm attains sample complexity polynomial in relevant problem parameters, and, by synthesizing locally stabilizing gains, overcomes exponential dependence in problem horizon. Experimental results validate the performance of our algorithm, and compare to natural deep-learning baselines.

Offline reinforcement learning (RL) allows robots to learn from offline datasets without risky exploration. Yet, offline RL's performance often hinges on a brittle trade-off between (1) return maximization, which can push policies outside the dataset support, and (2) behavioral constraints, which typically require sensitive hyperparameter tuning. Latent steering offers a structural way to stay within the dataset support during RL, but existing offline adaptations commonly approximate action values using latent-space critics learned via indirect distillation, which can lose information and hinder convergence. We propose Latent Policy Steering (LPS), which enables high-fidelity latent policy improvement by backpropagating original-action-space Q-gradients through a differentiable one-step MeanFlow policy to update a latent-action-space actor. By eliminating proxy latent critics, LPS allows an original-action-space critic to guide end-to-end latent-space optimization, while the one-step MeanFlow policy serves as a behavior-constrained generative prior. This decoupling yields a robust method that works out-of-the-box with minimal tuning. Across OGBench and real-world robotic tasks, LPS achieves state-of-the-art performance and consistently outperforms behavioral cloning and strong latent steering baselines.

Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable trade-off between passenger comfort and travel time. The problem is an instance of infinite dimensional optimization over two continuous functions: a path, and a velocity profile. We propose a simplification of this problem that facilitates the discretization of both functions. This paper also proposes a method to quickly generate minimal-length paths between start and goal states based on a single tuning parameter: the second derivative of curvature. Furthermore, we discretize the set of velocity profiles along a given path into a selection of acceleration way-points along the path. Gradient-descent is then employed to minimize cost over feasible choices of the second derivative of curvature, and acceleration way-points, resulting in a method that repeatedly solves the path and velocity profiles in an iterative fashion. Numerical examples are provided to illustrate the benefits of the proposed methods.

We consider the problem of preference based reinforcement learning (PbRL), where, unlike traditional reinforcement learning, an agent receives feedback only in terms of a 1 bit (0/1) preference over a trajectory pair instead of absolute rewards for them. The success of the traditional RL framework crucially relies on the underlying agent-reward model, which, however, depends on how accurately a system designer can express an appropriate reward function and often a non-trivial task. The main novelty of our framework is the ability to learn from preference-based trajectory feedback that eliminates the need to hand-craft numeric reward models. This paper sets up a formal framework for the PbRL problem with non-markovian rewards, where the trajectory preferences are encoded by a generalized linear model of dimension d. Assuming the transition model is known, we then propose an algorithm with almost optimal regret guarantee of mathcal{O}left( SH d log (T / delta) T right). We further, extend the above algorithm to the case of unknown transition dynamics, and provide an algorithm with near optimal regret guarantee mathcal{O}((d + H^2 + |S|)dT +|mathcal{S||A|TH} ). To the best of our knowledge, our work is one of the first to give tight regret guarantees for preference based RL problems with trajectory preferences.

Recent advances in inference-time scaling have significantly improved the reasoning performance of large language models (LLMs). However, these methods typically rely on repeated generation or external verification. To address this limitation, we introduce CritICL, a novel inference-time framework that improves reasoning while maintaining high efficiency. Our key insight is that LLM failure modes exhibit structured patterns across model scales within the same family. Instead of treating failures as undesirable outputs, CritICL leverages them as a source of guidance. Specifically, we utilize failure modes derived from weaker models and incorporate them into inference through critique-based in-context examples. We propose two variants: CritICL-dynamic, which adaptively predicts input-specific failure modes and retrieves critiques, and CritICL-static, which uses a global failure mode profile to provide stable guidance. Experimental results show that CritICL consistently outperforms standard in-context learning and achieves performance competitive with or superior to test-time scaling methods, while requiring significantly fewer generations and lower token cost. Code available at: https://github.com/umwyf/CRITICL

Although recent tool-augmented benchmarks involve complex requests, evaluation remains limited to answer matching, neglecting critical trajectory aspects like efficiency, hallucination, and adaptivity. The most straightforward method for evaluation is to compare an agent's trajectory with the ground-truth, but annotating all valid ground-truth trajectories is prohibitively expensive. In this manner, we introduce TRACE, a reference-free framework for the multi-dimensional evaluation of tool-augmented LLMs. By incorporating an evidence bank which accumulates knowledge from preceding steps, TRACE assesses an agent's reasoning trajectory effectively. To validate our framework, we develop a new meta-evaluation dataset with diverse and flawed trajectories, each labeled with multi-faceted performance scores. Our results confirm that TRACE accurately evaluates complex trajectories even with small open-source LLMs. Furthermore, we apply our method to evaluate the trajectories that agents produce while solving tool-augmented tasks, presenting previously unreported observations and their corresponding insights.

The objective function used in trajectory optimization is often non-convex and can have an infinite set of local optima. In such cases, there are diverse solutions to perform a given task. Although there are a few methods to find multiple solutions for motion planning, they are limited to generating a finite set of solutions. To address this issue, we presents an optimization method that learns an infinite set of solutions in trajectory optimization. In our framework, diverse solutions are obtained by learning latent representations of solutions. Our approach can be interpreted as training a deep generative model of collision-free trajectories for motion planning. The experimental results indicate that the trained model represents an infinite set of homotopic solutions for motion planning problems.

The recent adoption of artificial intelligence in socio-technical systems raises concerns about the black-box nature of the resulting decisions in fields such as hiring, finance, admissions, etc. If data subjects -- such as job applicants, loan applicants, and students -- receive an unfavorable outcome, they may be interested in algorithmic recourse, which involves updating certain features to yield a more favorable result when re-evaluated by algorithmic decision-making. Unfortunately, when individuals do not fully understand the incremental steps needed to change their circumstances, they risk following misguided paths that can lead to significant, long-term adverse consequences. Existing recourse approaches focus exclusively on the final recourse goal but neglect the possible incremental steps to reach the goal with real-life constraints, user preferences, and model artifacts. To address this gap, we formulate a visual analytic workflow for incremental recourse planning in collaboration with AI/ML experts and contribute an interactive visualization interface that helps data subjects efficiently navigate the recourse alternatives and make an informed decision. We present a usage scenario and subjective feedback from observational studies with twelve graduate students using a real-world dataset, which demonstrates that our approach can be instrumental for data subjects in choosing a suitable recourse path.

Reinforcement learning with verifiable rewards (RLVR) has become a core post-training recipe. Introducing suitable off-policy trajectories into on-policy exploration accelerates RLVR convergence and raises the performance ceiling, yet finding a source of such trajectories remains the key challenge. Existing mixed-policy methods either import trajectories from external teachers (high-quality but distributionally far) or replay past training trajectories (close but capped in quality), and neither simultaneously satisfies the strong enough (higher Q , more new knowledge to learn) and close enough (lower V , more readily absorbed) conditions required to maximize the effective learning signal S = Q/V. We propose Near-Future Policy Optimization (NPO), a simple mixed-policy scheme that learns from a policy's own near-future self: a later checkpoint from the same training run is a natural source of auxiliary trajectories that is both stronger than the current policy and closer than any external source, directly balancing trajectory quality against variance cost. We validate NPO through two manual interventions, early-stage bootstrapping and late-stage plateau breakthrough, and further propose AutoNPO,an adaptive variant that automatically triggers interventions from online training signals and selects the guide checkpoint that maximizes S. On Qwen3-VL-8B-Instruct with GRPO, NPO improves average performance from 57.88 to 62.84, and AutoNPO pushes it to 63.15, raising the final performance ceiling while accelerating convergence.

Building systems that are good for society in the face of complex societal effects requires a dynamic approach. Recent approaches to machine learning (ML) documentation have demonstrated the promise of discursive frameworks for deliberation about these complexities. However, these developments have been grounded in a static ML paradigm, leaving the role of feedback and post-deployment performance unexamined. Meanwhile, recent work in reinforcement learning has shown that the effects of feedback and optimization objectives on system behavior can be wide-ranging and unpredictable. In this paper we sketch a framework for documenting deployed and iteratively updated learning systems, which we call Reward Reports. Taking inspiration from various contributions to the technical literature on reinforcement learning, we outline Reward Reports as living documents that track updates to design choices and assumptions behind what a particular automated system is optimizing for. They are intended to track dynamic phenomena arising from system deployment, rather than merely static properties of models or data. After presenting the elements of a Reward Report, we discuss a concrete example: Meta's BlenderBot 3 chatbot. Several others for game-playing (DeepMind's MuZero), content recommendation (MovieLens), and traffic control (Project Flow) are included in the appendix.

Critique ability, a meta-cognitive capability of humans, presents significant challenges for LLMs to improve. Recent works primarily rely on supervised fine-tuning (SFT) using critiques generated by a single LLM like GPT-4. However, these model-generated critiques often exhibit flaws due to the inherent complexity of the critique. Consequently, fine-tuning LLMs on such flawed critiques typically limits the model's performance and propagates these flaws into the learned model. To overcome these challenges, this paper proposes a novel data generation pipeline, named MultiCritique, that improves the critique ability of LLMs by utilizing multi-agent feedback in both the SFT and reinforcement learning (RL) stages. First, our data generation pipeline aggregates high-quality critiques from multiple agents instead of a single model, with crucial information as input for simplifying the critique. Furthermore, our pipeline improves the preference accuracy of critique quality through multi-agent feedback, facilitating the effectiveness of RL in improving the critique ability of LLMs. Based on our proposed MultiCritique data generation pipeline, we construct the MultiCritiqueDataset for the SFT and RL fine-tuning stages. Extensive experimental results on two benchmarks demonstrate: 1) the superior quality of our constructed SFT dataset compared to existing critique datasets; 2) additional improvements to the critique ability of LLMs brought by the RL stage. Notably, our fine-tuned 7B model significantly surpasses other advanced 7B-13B open-source models, approaching the performance of advanced 70B LLMs and GPT-4. Codes, datasets and model weights will be publicly available.

Large Language Models (LLMs) have demonstrated remarkable capabilities, enabling language agents to excel at single-turn tasks. However, their application to complex, multi-step, and long-horizon tasks remains challenging. While reinforcement learning (RL) offers a promising avenue for addressing these challenges, mainstream approaches typically rely solely on sparse, outcome-based rewards, a limitation that becomes especially problematic for group-based RL algorithms lacking critic models, such as Group Relative Policy Optimization (GRPO). In such methods, uniformly rewarding or penalizing all actions within a trajectory can lead to training instability and suboptimal policies, because beneficial and detrimental actions are often entangled across multi-step interactions. To address this challenge, we propose SALT, a novel and lightweight framework that provides a finer-grained advantage assignment, derived solely from outcome rewards. We achieve this by constructing a graph from trajectories of the same prompt, which allows us to quantify the quality of each step and assign advantages accordingly. Crucially, SALT is designed as a plug-and-play module that seamlessly integrates with existing group-based RL algorithms, requiring no modifications to the rollout procedure and introducing negligible computational overhead. Extensive experiments on the WebShop, ALFWorld, and AppWorld benchmarks with various model sizes demonstrate that SALT consistently improves performance. We also conduct a thorough analysis to validate the design choices behind SALT and offer actionable insights.

Failure attribution for LLM-based agentic systems, i.e., identifying which steps in a failure trajectory caused the task to fail, is critical for debugging and improving these systems. Existing approaches either rely on prompting-based pipelines, which are computationally expensive, or require post-training on failure trajectories with step-level error annotations, which are costly to collect and difficult to scale. We argue that a practical failure attribution model should be lightweight and trainable without step-level supervision on failure data. To this end, we address unsupervised failure attribution, i.e., training exclusively on successful trajectories and identifying error steps at inference time given a failure trajectory. We propose OAT, which casts this problem as one-class learning with neural controlled differential equations, modeling the dynamical pattern of successful trajectories in latent space. At inference time, each step in a failure trajectory is assigned an anomaly score based on its deviation from the dynamics learned on successful trajectories, which is then used to form a set of error steps. With training on only 100 successful trajectories, experiments show that OAT is 200--5000 times faster than prompting-based baselines, and, at the same time, consistently outperforms them in both in-domain and out-of-distribution datasets with +20% and +7% F1 scores, respectively, demonstrating that OAT is a promising and efficient direction for diagnosing agentic system failures.

Subjective multi-turn dialogue tasks, such as emotional support, require conversational policies that adapt to evolving user states and optimize long-horizon interaction quality. However, reinforcement learning (RL) for such settings remains challenging due to the absence of reliable process supervision. Outcome-only training collapses credit assignment across turns into a single trajectory-level reward, while naïve turn-level group sampling incurs prohibitive rollout costs in interactive environments. We propose a critic-free and efficient RL algorithm named MAPO that leverages dense process feedback from a judge model and propagates long-horizon effects through Monte Carlo returns. To stabilize optimization, we introduce a mixed advantage estimator that combines turn-level normalization with batch-level normalization, enabling fine-grained yet scalable credit assignment. Across multiple subjective dialogue benchmarks, including EMPA, EmoBench, and EQ-Bench, and model scales ranging from 7B to 32B, our method consistently improves both training stability and final performance over outcome-only GRPO and single-level normalization baselines. On EMPA, we improve rates by up to 9 points and increase dialogue scores by as much as +43.2 over the 7B base model. Despite training only on EMPA-style environments, our approach generalizes well, yielding consistent improvements on unseen emotional-intelligence benchmarks, including up to +4 points on EmoBench and +3.5 on EQ-Bench. Together, these results demonstrate that dense process supervision combined with mixed-level normalization enables effective and scalable RL for subjective, open-ended multi-turn dialogue.

Traditional theories of optimization cannot describe the dynamics of optimization in deep learning, even in the simple setting of deterministic training. The challenge is that optimizers typically operate in a complex, oscillatory regime called the "edge of stability." In this paper, we develop theory that can describe the dynamics of optimization in this regime. Our key insight is that while the *exact* trajectory of an oscillatory optimizer may be challenging to analyze, the *time-averaged* (i.e. smoothed) trajectory is often much more tractable. To analyze an optimizer, we derive a differential equation called a "central flow" that characterizes this time-averaged trajectory. We empirically show that these central flows can predict long-term optimization trajectories for generic neural networks with a high degree of numerical accuracy. By interpreting these central flows, we are able to understand how gradient descent makes progress even as the loss sometimes goes up; how adaptive optimizers "adapt" to the local loss landscape; and how adaptive optimizers implicitly navigate towards regions where they can take larger steps. Our results suggest that central flows can be a valuable theoretical tool for reasoning about optimization in deep learning.

In meta reinforcement learning (meta RL), an agent learns from a set of training tasks how to quickly solve a new task, drawn from the same task distribution. The optimal meta RL policy, a.k.a. the Bayes-optimal behavior, is well defined, and guarantees optimal reward in expectation, taken with respect to the task distribution. The question we explore in this work is how many training tasks are required to guarantee approximately optimal behavior with high probability. Recent work provided the first such PAC analysis for a model-free setting, where a history-dependent policy was learned from the training tasks. In this work, we propose a different approach: directly learn the task distribution, using density estimation techniques, and then train a policy on the learned task distribution. We show that our approach leads to bounds that depend on the dimension of the task distribution. In particular, in settings where the task distribution lies in a low-dimensional manifold, we extend our analysis to use dimensionality reduction techniques and account for such structure, obtaining significantly better bounds than previous work, which strictly depend on the number of states and actions. The key of our approach is the regularization implied by the kernel density estimation method. We further demonstrate that this regularization is useful in practice, when `plugged in' the state-of-the-art VariBAD meta RL algorithm.

Discrete-action reinforcement learning algorithms often falter in tasks with high-dimensional discrete action spaces due to the vast number of possible actions. A recent advancement leverages value-decomposition, a concept from multi-agent reinforcement learning, to tackle this challenge. This study delves deep into the effects of this value-decomposition, revealing that whilst it curtails the over-estimation bias inherent to Q-learning algorithms, it amplifies target variance. To counteract this, we present an ensemble of critics to mitigate target variance. Moreover, we introduce a regularisation loss that helps to mitigate the effects that exploratory actions in one dimension can have on the value of optimal actions in other dimensions. Our novel algorithm, REValueD, tested on discretised versions of the DeepMind Control Suite tasks, showcases superior performance, especially in the challenging humanoid and dog tasks. We further dissect the factors influencing REValueD's performance, evaluating the significance of the regularisation loss and the scalability of REValueD with increasing sub-actions per dimension.

Large language models (LLMs) have recently transformed from text-based assistants to autonomous agents capable of planning, reasoning, and iteratively improving their actions. While numerical reward signals and verifiers can effectively rank candidate actions, they often provide limited contextual guidance. In contrast, natural language feedback better aligns with the generative capabilities of LLMs, providing richer and more actionable suggestions. However, parsing and implementing this feedback effectively can be challenging for LLM-based agents. In this work, we introduce Critique-Guided Improvement (CGI), a novel two-player framework, comprising an actor model that explores an environment and a critic model that generates detailed nature language feedback. By training the critic to produce fine-grained assessments and actionable revisions, and the actor to utilize these critiques, our approach promotes more robust exploration of alternative strategies while avoiding local optima. Experiments in three interactive environments show that CGI outperforms existing baselines by a substantial margin. Notably, even a small critic model surpasses GPT-4 in feedback quality. The resulting actor achieves state-of-the-art performance, demonstrating the power of explicit iterative guidance to enhance decision-making in LLM-based agents.

Reinforcement learning with verifiable rewards (RLVR) has become a core technique for post-training of Large Language Models (LLMs). While policy optimization is driven by all sampled tokens under a globally broadcast scalar reward, the heterogeneous policy behaviors exhibited along trajectories are largely overlooked without differentiation. Existing works address this by credit allocation, including token-level advantage reweighting, and selective token optimization, however, the allocation criterion are principally stagnant throughout training, limiting resilient policy evolution. In this work, we argue that when learning signals are scheduled can be as important as where they are allocated across tokens, and introduce the temporal dimension that scheduling the credit allocation criteria over the course of RLVR optimization. We find that prioritizing targeted tokens emphasized with specific policy behaviors, and gradually attenuating toward general optimization leads to more stable and efficient learning dynamics. Furthermore, we show that simple trajectory percentiles provide a natural perspective for distinguishing policy behaviors, and works effectively with temporal scheduling. Our analysis reveals that standard optimization substantially sacrifices policy entropy when simultaneously accommodating heterogeneous behaviors, whereas temporal scheduling yields healthier policy evolution dynamics. Experiments across mathematical and general reasoning benchmarks demonstrate consistent improvements, suggesting that temporal scheduling constitutes a promising optimization dimension.

We present Self-Play Preference Optimization (SPO), an algorithm for reinforcement learning from human feedback. Our approach is minimalist in that it does not require training a reward model nor unstable adversarial training and is therefore rather simple to implement. Our approach is maximalist in that it provably handles non-Markovian, intransitive, and stochastic preferences while being robust to the compounding errors that plague offline approaches to sequential prediction. To achieve the preceding qualities, we build upon the concept of a Minimax Winner (MW), a notion of preference aggregation from the social choice theory literature that frames learning from preferences as a zero-sum game between two policies. By leveraging the symmetry of this game, we prove that rather than using the traditional technique of dueling two policies to compute the MW, we can simply have a single agent play against itself while maintaining strong convergence guarantees. Practically, this corresponds to sampling multiple trajectories from a policy, asking a rater or preference model to compare them, and then using the proportion of wins as the reward for a particular trajectory. We demonstrate that on a suite of continuous control tasks, we are able to learn significantly more efficiently than reward-model based approaches while maintaining robustness to the intransitive and stochastic preferences that frequently occur in practice when aggregating human judgments.

Extending the capabilities of Large Language Models (LLMs) with functions or tools for environment interaction has led to the emergence of the agent paradigm. In industry, training an LLM is not always feasible because of the scarcity of domain data, legal holds on proprietary customer data, rapidly changing business requirements, and the need to prototype new assistants. Agents provide an elegant solution to the above by relying on the zero-shot reasoning abilities of the underlying LLM and utilizing tools to explore and reason over customer data and respond to user requests. However, there are two concerns here: (I) acquiring large scale customer queries for agent testing is time-consuming, and (II) high reliance on the tool call sequence (or trajectory) followed by the agent to respond to user queries may lead to unexpected or incorrect behavior. To address this, we propose MAG-V, a multi-agent framework to first generate a dataset of questions that mimic customer queries; and second, reverse-engineer alternate questions from the responses for trajectory verification. Initial results indicate that our synthetic data can improve agent performance on actual customer queries. Furthermore, our trajectory verification methodology, inspired by distant supervision and using traditional machine learning (ML) models, outperforms a GPT-4o judge baseline by 11% accuracy and matches the performance of a GPT-4 judge on our constructed dataset. Overall, our approach is a step towards unifying diverse task agents into a cohesive framework for achieving an aligned objective.

In vision-language modeling, critic models are typically trained to evaluate outputs -- assigning scalar scores or pairwise preferences -- rather than to generate responses. This separation from policy models, which produce the responses, is so entrenched that critics are rarely considered for direct policy use. In this work, we challenge this convention. We propose to reorganize preference-labeled critic datasets into verifiable training signals and perform reinforcement learning directly on a base generative model, producing LLaVA-Critic-R1, a multimodal critic trained to optimize preference judgments while retaining full generation ability. Surprisingly, LLaVA-Critic-R1 emerges not only as a top-performing critic but also as a competitive policy model -- matching or surpassing specialized reasoning VLMs trained with in-domain data across 26 visual reasoning and understanding benchmarks, with an average gain of +5.7% over its base model (Qwen-2.5-VL-7B). Extending this approach to existing strong reasoning VLMs yields LLaVA-Critic-R1+, which further advances policy performance without sacrificing critic quality, achieving a SoTA performance of 71.9 on MMMU at the 7B scale. Finally, we show that the enhanced critic ability benefits inference: applying self-critique at test time yields an average +13.8% improvement on five representative reasoning tasks without additional training. Our results reveal that RL training on critic data can produce a unified model excelling at both evaluation and generation, offering a simple path toward scalable, self-improving multimodal systems.

Joint-Embedding Predictive Architectures (JEPAs) learn world models by predicting in representation space rather than reconstructing pixels, making them a natural backbone for latent model predictive control from offline demonstration logs. JEPA-style training optimizes short-horizon latent prediction, whereas planning requires a multi-step ranking of imagined futures by goal progress. Prior JEPA planners often inherit that ranking from embedding geometry, typically latent Euclidean distance, which arises as a byproduct of representation learning rather than as a progress cost mined from the logs. We propose temporal-distance JEPA (TD-JEPA), which retains the LeWM encoder--predictor backbone and mines a directed temporal cost from reward-free trajectories: same-trajectory step order supplies positive targets, cross-trajectory pairs act as heuristic negatives, and a rollout-consistency term matches the planner horizon. The mined supervision serves two roles: as the deployed planning cost when progress is topological, and as a representation signal that improves Euclidean planning when contact geometry dominates. Under locked evaluation, deploying the mined cost raises Two-Room success to 100.0% versus LeWM's 97.4%, while shared Euclidean planning on the same temporally trained checkpoint raises OGB-Cube by 14.2 points over LeWM and improves Push-T. Against LeWM and the concurrent RC-aux baseline under locked evaluation, TD-JEPA matches or exceeds both methods on every environment. Ablations show that the directed head, cross-trajectory negatives, and rollout consistency each contribute. TD-JEPA narrows the train--plan gap for JEPA world-model planners by discovering temporal progress structure in offline logs and co-designing cost form with plan-time deployment. Code is available at https://github.com/HKBU-KnowComp/TD-JEPA.

Temporal-difference (TD) methods learn state and action values efficiently by bootstrapping from their own future value predictions, but such a self-bootstrapping mechanism is prone to bootstrapping bias, where the errors in the value targets accumulate across steps and result in biased value estimates. Recent work has proposed to use chunked critics, which estimate the value of short action sequences ("chunks") rather than individual actions, speeding up value backup. However, extracting policies from chunked critics is challenging: policies must output the entire action chunk open-loop, which can be sub-optimal for environments that require policy reactivity and also challenging to model especially when the chunk length grows. Our key insight is to decouple the chunk length of the critic from that of the policy, allowing the policy to operate over shorter action chunks. We propose a novel algorithm that achieves this by optimizing the policy against a distilled critic for partial action chunks, constructed by optimistically backing up from the original chunked critic to approximate the maximum value achievable when a partial action chunk is extended to a complete one. This design retains the benefits of multi-step value propagation while sidestepping both the open-loop sub-optimality and the difficulty of learning action chunking policies for long action chunks. We evaluate our method on challenging, long-horizon offline goal-conditioned tasks and show that it reliably outperforms prior methods. Code: github.com/ColinQiyangLi/dqc.

Offline reinforcement learning (RL) can fail spectacularly when bootstrapped temporal-difference (TD) updates amplify their own errors, driving the critic toward extreme and unusable Q-values. A key counterintuitive insight of this work is that collapse is not only a property of the backup rule or network architecture: optimizer dynamics themselves can directly trigger or suppress instability. From a control-theoretic viewpoint, we model offline TD learning as a feedback system and analyze Adam-based critic updates. This yields a necessary and sufficient condition for stability of the induced local update dynamics: within the regime we analyze, these dynamics are stable if and only if the spectral radius of the corresponding update operator is strictly below one. Further analysis suggests that standard Adam updates can inadvertently distort the parameter geometry, motivating explicit orthogonality constraints to prevent TD error amplification. To this end, we propose AdamO, an Adam-based optimizer with a decoupled orthogonality correction regulated by a strict task-alignment budget. We prove that this design theoretically guarantees worst-case task safety and preserves Adam's continuous-time dissipative dynamics. Empirically, AdamO is broadly compatible with diverse offline RL baselines, improving stability and returns across a broad suite of benchmarks.

Reinforcement Learning Fine-Tuning (RLFT) has achieved notable success in tasks with objectively verifiable answers (e.g., code generation, mathematical reasoning), yet struggles with open-ended subjective tasks like role-playing dialogue. Traditional reward modeling approaches, which rely on independent sample-wise scoring, face dual challenges: subjective evaluation criteria and unstable reward signals.Motivated by the insight that human evaluation inherently combines explicit criteria with implicit comparative judgments, we propose Comparative Policy Optimization (CPO). CPO redefines the reward evaluation paradigm by shifting from sample-wise scoring to comparative group-wise scoring.Building on the same principle, we introduce the CharacterArena evaluation framework, which comprises two stages:(1) Contextualized Multi-turn Role-playing Simulation, and (2) Trajectory-level Comparative Evaluation. By operationalizing subjective scoring via objective trajectory comparisons, CharacterArena minimizes contextual bias and enables more robust and fair performance evaluation. Empirical results on CharacterEval, CharacterBench, and CharacterArena confirm that CPO effectively mitigates reward ambiguity and leads to substantial improvements in dialogue quality.

Developing multi-turn interactive tool-use agents is challenging because real-world user needs are often complex and ambiguous, yet agents must execute deterministic actions to satisfy them. To address this gap, we introduce CoVe (Constraint-Verification), a post-training data synthesis framework designed for training interactive tool-use agents while ensuring both data complexity and correctness. CoVe begins by defining explicit task constraints, which serve a dual role: they guide the generation of complex trajectories and act as deterministic verifiers for assessing trajectory quality. This enables the creation of high-quality training trajectories for supervised fine-tuning (SFT) and the derivation of accurate reward signals for reinforcement learning (RL). Our evaluation on the challenging τ^2-bench benchmark demonstrates the effectiveness of the framework. Notably, our compact CoVe-4B model achieves success rates of 43.0\% and 59.4\% in the Airline and Retail domains, respectively; its overall performance significantly outperforms strong baselines of similar scale and remains competitive with models up to 17times its size. These results indicate that CoVe provides an effective and efficient pathway for synthesizing training data for state-of-the-art interactive tool-use agents. To support future research, we open-source our code, trained model, and the full set of 12K high-quality trajectories used for training.

The ability of large language models (LLMs) to utilize external tools has enabled them to tackle an increasingly diverse range of tasks. However, as the tasks become more complex and long-horizon, the intricate tool utilization process may trigger various unexpected errors. Therefore, how to effectively handle such errors, including identifying, diagnosing, and recovering from them, has emerged as a key research direction for advancing tool learning. In this work, we first extensively analyze the types of errors encountered during the function-calling process on several competitive tool evaluation benchmarks. Based on it, we introduce CRITICTOOL, a comprehensive critique evaluation benchmark specialized for tool learning. Building upon a novel evolutionary strategy for dataset construction, CRITICTOOL holds diverse tool-use errors with varying complexities, which better reflects real-world scenarios. We conduct extensive experiments on CRITICTOOL, and validate the generalization and effectiveness of our constructed benchmark strategy. We also provide an in-depth analysis of the tool reflection ability on various LLMs, offering a new perspective on the field of tool learning in LLMs. The code is available at https://github.com/Shellorley0513/CriticTool{https://github.com/Shellorley0513/CriticTool}.

Reinforcement Learning (RL) has emerged as a popular training paradigm, particularly when paired with reasoning models. While effective, it primarily focuses on generating responses and lacks mechanisms to explicitly foster critique or reflection. Several recent studies, like Critique-Fine-Tuning (CFT) and Critique-Guided-Distillation (CGD) have shown the benefits of explicitly teaching LLMs how to critique. Motivated by them, we propose Critique Reinforcement Learning (CRL), where the model is tasked with generating a critique for a given (question, solution) pair. The reward is determined solely by whether the final judgment label c in {True, False} of the generated critique aligns with the ground-truth judgment c^*. Building on this point, we introduce Critique-Coder, which is trained on a hybrid of RL and CRL by substituting 20\% of the standard RL data with CRL data. We fine-tune multiple models (Critique-Coder) and evaluate them on different benchmarks to show their advantages over RL-only models. We show that Critique-Coder consistently outperforms RL-only baselines on all the evaluated benchmarks. Notably, our Critique-Coder-8B can reach over 60\% on LiveCodeBench (v5), outperforming other reasoning models like DeepCoder-14B and GPT-o1. Beyond code generation, Critique-Coder also demonstrates enhanced general reasoning abilities, as evidenced by its better performance on logic reasoning tasks from the BBEH dataset. This indicates that the application of CRL on coding datasets enhances general reasoning and critique abilities, which are transferable across a broad range of tasks. Hence, we believe that CRL works as a great complement to standard RL for LLM reasoning.

Recent advances in reinforcement learning for foundation models, such as Group Relative Policy Optimization (GRPO), have significantly improved the performance of foundation models on reasoning tasks. Notably, the advantage function serves as a central mechanism in GRPO for ranking the trajectory importance. However, existing explorations encounter both advantage reversion and advantage mirror problems, which hinder the reasonable advantage allocation across different query samples. In this work, we propose an easy but effective GRPO strategy, Mixed Advantage Policy Optimization (MAPO). We reveal that the trajectory appears with different certainty and propose the advantage percent deviation for samples with high-certainty trajectories. Furthermore, we dynamically reweight the advantage function for samples with varying trajectory certainty, thereby adaptively configuring the advantage function to account for sample-specific characteristics. Comparison with related state-of-the-art methods, along with ablation studies on different advantage variants, validates the effectiveness of our approach.

Self-critic has become an important mechanism for enhancing the reasoning performance of LLMs. However, current approaches mainly involve basic prompts without further training, which tend to be over-simplified, leading to limited accuracy.Moreover, there is a lack of in-depth investigation of the relationship between LLM's ability to criticism and its task-solving performance.To address these issues, we propose Critic-CoT, a novel framework that pushes LLMs toward System-2-like critic capability, via step-wise CoT reasoning format and distant-supervision data construction, without the need for human annotation. Experiments on GSM8K and MATH show that via filtering out invalid solutions or iterative refinement, our enhanced model boosts task-solving performance, which demonstrates the effectiveness of our method. Further, we find that training on critique and refinement alone improves the generation. We hope our work could shed light on future research on improving the reasoning and critic ability of LLMs.

In value-based reinforcement learning methods such as deep Q-learning, function approximation errors are known to lead to overestimated value estimates and suboptimal policies. We show that this problem persists in an actor-critic setting and propose novel mechanisms to minimize its effects on both the actor and the critic. Our algorithm builds on Double Q-learning, by taking the minimum value between a pair of critics to limit overestimation. We draw the connection between target networks and overestimation bias, and suggest delaying policy updates to reduce per-update error and further improve performance. We evaluate our method on the suite of OpenAI gym tasks, outperforming the state of the art in every environment tested.