Critic-Free RL

Asynchronous reinforcement learning (RL) for large language model (LLM) agents trains one policy on trajectories generated by another: rollouts come from stale checkpoints, and the inference engine's probabilities differ from the trainer's even at identical parameters. Standard remedies either clip importance ratios, which biases the update, or, as in GRPO, sample a group of responses per prompt, which is costly when episodes are long. We propose KL-Regularized Policy Optimization (KLPO), a framework that anchors the KL regularizer at the sampler. The regularized improvement step then has a closed-form Gibbs solution, and KLPO fits its log-ratio optimality condition by least squares on the sampler's own trajectories, so the sampler probability enters through a log-ratio and no importance weights are needed. Profiling out the regression intercept replaces the intractable log-partition function with the signal's sampler mean plus a sampler-to-trainer KL divergence. For token-level policy mirror descent targets, we show that the resulting gradient can be computed from terminal returns without a critic, via sampler-centered scores or a single trajectory residual, even under stochastic tool outputs. We further prove that independent Monte Carlo estimates of the KL term keep these gradients unbiased, derive the exact KL gap of cheaper top-$K$ and binary approximations, and show that SPPO, GPO, REBEL, and BPO arise as special cases of KLPO. The result is a critic-free update that uses one rollout per prompt and requires neither a learned normalizer nor a group of responses.

Group Relative Policy Optimization (GRPO) avoids a separate critic by estimating advantages from rollout groups. For multi-turn agents, however, trajectory-level supervision provides coarse, noisy credit: terminal rewards do not locate errors and can penalize useful actions alongside mistakes. Group-in-Group Policy Optimization (GiGPO) and subsequent methods refine supervision through state-conditioned comparisons, but their credit estimates remain sensitive to downstream decisions and outcomes. We introduce RELACE, Retrospective Likelihood-based Action, a critic-free framework that integrates retrospective action assessment with state-conditioned advantage estimation. RELACE evaluates executed actions through teacher-forced likelihood scoring under both their original contexts and outcome-augmented contexts. Comparing these likelihoods yields a trajectory-normalized retrospective factor that captures outcome-dependent changes in action plausibility, rather than hindsight plausibility alone. We use this factor to reweight discounted task returns and construct local advantages by comparing weighted returns among actions from equivalent states within a task. This couples retrospective relevance with observed reward, producing fine-grained credit that complements trajectory-level GRPO supervision. Temporal smoothing and success-protecting masking further stabilize the local signal. RELACE requires neither auxiliary value nor reward models nor additional autoregressive rollouts for credit estimation. Experiments on ALFWorld and WebShop with Qwen2.5-1.5B-Instruct and Qwen2.5-7B-Instruct demonstrate substantial improvements over GRPO, GiGPO, and HCAPO. With the 1.5B model, RELACE achieves $96.35\%$ success on ALFWorld and $79.43\%$ on WebShop, surpassing GiGPO by $5.47$ and $5.60$ percentage points, respectively.

Group-based reinforcement learning such as GRPO trains LLM agents by comparing rollouts sampled for each task, without a learned critic. In long-horizon settings, these rollouts revisit shared anchor states, offering cross-rollout evidence for step-level credit. Ideally, step-level credit should incorporate evidence beyond the realized suffixes observed at an anchor while aggregating alternative continuations according to their empirical frequencies. Visit-local averaging pools realized suffix returns at shared anchors and respects observed frequencies, but does not recursively propagate evidence across rollouts, whereas shortest-path estimators have global reach but allow a rarely observed route to dominate an anchor's value. We introduce Cross-Rollout Bellman Closure (CRBC), which merges each rollout group into a finite empirical process with absorbing success and failure boundaries and evaluates its behavior-policy Bellman fixed point with one linear solve. This fixed point uses the same empirical action and transition frequencies to propagate evidence through shared anchors and aggregate alternative continuations. Backing up the resulting state values through observed transitions yields action values, whose gain over the corresponding state value provides step-level credit. A corresponding finite-depth family recovers visit-local return averaging at zero depth and converges to the exact closure as depth increases. The normalized closure credit is combined with the trajectory-level group advantage for policy optimization, without additional environment rollouts. Across ALFWorld, WebShop, and Sokoban benchmarks with multiple model scales, CRBC consistently improves final performance and learning efficiency. For example, CRBC outperforms the strongest evaluated baseline by 5.59 percentage points on ALFWorld with Qwen2.5-1.5B-Instruct.

Actor-critic architecture has been widely used in continuous robot control. However, they rely on learning a value network, introducing additional computational overhead during training. Moreover, policy learning may also be affected by the approximation error of value estimation. Critic-free group relative policy optimization methods provide a simpler training approach by removing the need for a critic. However, they fail to learn long-term action outcomes when directly applying immediate rewards to policy optimization in dense-reward environments. To address these problems, we propose Group Relative Return Policy Optimization (GR2PO), a critic-free reinforcement learning framework for continuous robot control. GR2PO estimates the discounted returns from the parallelly collected trajectories, performs group normalization at each rollout time index, and uses relative advantages and clipped targets to update the policy. To evaluate the effectiveness of the proposed framework, we instantiate it on robot control simulation environments and deploy the model to a real-world edge device. The results show that GR2PO significantly outperforms critic-free baselines that use immediate rewards and performs competitively against state-of-the-art actor-critic methods. Furthermore, GR2PO demonstrates competitive training efficiency. Inference tests on NVIDIA Jetson TX2 demonstrate the feasibility of deploying the learned policies on edge platforms. Further ablation experiments analyze the effects of parallel group size, return estimation methods, and target clipping ratio on learning performance. To support follow-up research, we will make the complete code publicly available after the paper is accepted, including the framework implementation, experimental configuration, and training and evaluation scripts.

Reinforcement learning with verifiable rewards (RLVR) improves the reasoning capabilities of large language models (LLMs). We introduce Bellman Policy Optimization (BPO), a critic-free method derived from Policy Mirror Descent (PMD). For autoregressive generation with terminal rewards, BPO uses the Bellman equations to reformulate PMD as a trajectory-level objective. The reformulation avoids estimating state values at intermediate states. We prove that it has the same unique optimal solution as the original PMD objective. We derive the practical BPO loss by approximating this objective. Its mismatch-correction weight is a smoothed ratio of complementary token probabilities. Experiments on mathematical reasoning benchmarks demonstrate the effectiveness of BPO.

Long-horizon language-model agents trained with reinforcement learning oftenreceive sparse outcome rewards that do not reveal which decisions along a tra-jectory deserve credit. Episode-level advantages provide coarse trajectory-widecredit, while step-level comparisons offer finer resolution with context-dependentestimation noise. We propose Granularity-Adaptive Credit Assignment (GACA),a critic-free method that adaptively mixes episode- and step-level credit for eachdecision during policy optimization. GACA normalizes the sampled response'smean per-token negative log-likelihood (NLL) within each trajectory and uses theresulting criticality score to determine the step-specific mixture. The computationreuses rollout log-probabilities without additional training rollouts or model eval-uations. Our analysis characterizes optimal score-dependent mixing and derivesconditions linking expected NLL to a lower bound on the preferred step-levelweight. Across ALFWorld and WebShop with 1.5B and 7B backbones, GACAachieves the highest reported mean success rates among the compared methods,while introducing negligible additional computation.

Offline-to-online (O2O) reinforcement learning aims to leverage policies pretrained on static datasets while improving them through online interaction. However, directly reusing an offline-trained critic can hinder online fine-tuning: as the policy and data distribution change rapidly, value estimates inherited from offline training may become misaligned with the online environment, leading to inaccurate policy improvement and inefficient exploration. To address this problem, we introduce Critic-Free Pretraining: an efficient paradigm that completely abandons the approach of offline critic training, allowing a freshly initialized critic to adapt without inheriting biased estimates. CFP is compatible with various mainstream O2O algorithms and consistently matches or improves upon conventional O2O algorithms across a diverse set of tasks, with particularly pronounced gains on several challenging tasks.

Reinforcement learning (RL) has achieved remarkable success in enhancing the reasoning capabilities of large language models (LLMs). However, widely used critic-free RL methods rely on uniform credit assignment, broadcasting the same advantage to all tokens regardless of their differences. We identify a critical failure mode of this design, which we refer to as Positive-Credit Contamination: low-probability tail tokens that are contextually erroneous receive identical positive credit to plausible ones within the same trajectory, resulting in the indiscriminate reinforcement of flawed reasoning behavior. To mitigate this issue, we propose Tail-Aware Credit calibratiOn (TACO), a method that calibrates uniform credit assignment to suppress undesirable positive updates. TACO first computes a tail-risk score that incorporates the local generation context to assess each token's risk of falling into the unreliable tail, distinguishing unexpected rarity from uncertainty-driven exploration. TACO then uses this score to tune positive credit for risky tokens without removing their gradients entirely, so that recurring useful rare patterns can accumulate reinforcement while incidental noise is progressively dampened. Experimental results across three LLMs and eight benchmarks show that TACO consistently outperforms GRPO-style baselines. Notably, TACO improves training stability, supporting sustained performance gains in long-horizon RL. The source code is available at: https://github.com/xiuyilou/TACO.

Reinforcement Learning from Human Feedback (RLHF) for Large Language Models increasingly relies on critic-free methods as a practical alternative to actor--critic training. Despite their simplicity, existing critic-free approaches propagate a trajectory-level learning signal uniformly across all tokens in a trajectory. This requires full-trajectory policy updates for every rollout, leading to substantial optimization cost for long reasoning traces, even though intermediate prefixes often contain enough information to largely determine the final outcome. We propose Prefix-Sampling Proximal Policy Optimization (PS-PPO), a compute-efficient critic-free method for RLHF that exploits this temporal redundancy. PS-PPO introduces a prompt-conditioned cutoff distribution and samples a cutoff timestep for each trajectory. During the update pass, PS-PPO backpropagates only through the sampled prefix of each trajectory and applies an importance-weighting correction so that the resulting truncated gradient estimator remains unbiased with respect to the full-trajectory objective. Experiments on mathematical reasoning and RLHF benchmarks show that PS-PPO achieves large reductions in training compute and peak GPU memory, while maintaining accuracy comparable to strong critic-free baselines.

Critic-free reinforcement learning with verifiable rewards (RLVR), exemplified by Group Relative Policy Optimization (GRPO), avoids training a value function (critic) and reduces memory and compute overhead relative to critic-based PPO pipelines for aligning large language models. However, GRPO-style advantage estimation depends on prompt-local (within-prompt-group) reward statistics and can be unstable. In particular, when all rollouts in a prompt group receive identical rewards, the within-group reward variance becomes zero, and group normalization yields zero advantages for that group, impeding learning in cold-start regimes with binary verifiers. We introduce BV-Blend, a critic-free framework that stabilizes advantage estimation by combining prompt-local on-policy statistics with semantic-cluster-conditioned historical moments. BV-Blend maintains EMA-tracked reward moments for each cluster, derives a confidence weight from a standard error of the mean (SEM) proxy, and uses this weight to blend historical and prompt-local baseline and variance statistics into a standardized advantage for PPO-style clipped updates. Experiments on verifiable reasoning benchmarks show that BV-Blend improves training stability and performance, and remains robust in regimes where group-normalized methods may stall.

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.

Reinforcement learning (RL) has become a central paradigm for post-training large language models. Existing critic-free RL methods typically generate a group of rollouts for the same question to estimate value baselines for advantage computation. However, this design suffers from data inefficiency, group synchronization barriers, and inflexibility with structured rollouts. In this work, we revisit the role of the ``group'' and show that its underlying function is not merely to estimate baselines but to prevent false penalties on negative samples. Building on this insight, we propose negative token filtering, a simple and effective strategy that enables stable single-rollout training. We apply it to two batch-level advantage methods, achieving comparable performance on reasoning tasks and stronger performance on agentic tasks relative to group-based RL techniques.

Reinforcement learning with verifiable rewards has become a standard recipe for improving the reasoning abilities of large language models. Existing algorithms face a tradeoff between computational efficiency and sample efficiency in value estimation and policy learning. We introduce BASIS, a critic-free post-training algorithm designed to address this tradeoff. At each online training step, BASIS samples only one rollout per prompt, but leverages rich information across prompts in the entire batch to improve value function estimation. Our experiments demonstrate that BASIS reduces MSE in value function estimation by 69% compared to REINFORCE++, a representative single-rollout baseline, and achieves lower MSE with one rollout than group mean estimators with 8 rollouts. This improvement in value estimation translates to better policy optimization: using substantially less training time, BASIS achieves performance close to multi-rollout GRPO-type baselines and often outperforms single-rollout REINFORCE-type baselines.

Reinforcement learning substantially improves pretrained language models, but it remains understudied why critic-free methods such as PPO and GRPO work as well as they do, and when they should provide the largest gains. We develop a value-gradient perspective of critic-free RL for LLM post-training. First, under a differentiable rollout and additive-noise parameterization, we show that the actor update is value-gradient-like in expectation: the backward pass propagates costates whose conditional expectation equals the value gradient. Second, for discrete transformer policies, we show that autodifferentiation through attention produces empirical costates that approximate this value signal, with an error controlled by the sampling gap and policy entropy. These results motivate a decomposition of RL impact into value gradient signal and reachable reward headroom, yielding a criterion for when RL should be most effective along a pretraining trajectory.

Reinforcement learning has become a powerful paradigm for post-training large language model agents, yet credit assignment in multi-turn environments remains a challenge. Agents often receive sparse, trajectory-level rewards only at the end of an episode, making it difficult to determine which intermediate actions contributed to success or failure. As a result, propagating delayed outcomes back to individual decision steps without relying on costly auxiliary value models remains an open problem. We propose Generalized Advantage Grouped Policy Optimization (GAGPO), a critic-free reinforcement learning method for precise, step-aligned temporal credit assignment. GAGPO constructs a non-parametric grouped value proxy from sampled rollouts and uses it to compute TD/GAE-style temporal advantages, recursively propagating outcome supervision backward through time. Combined with group-wise advantage normalization and an action-level importance ratio, GAGPO extracts stable, localized optimization signals directly from multi-turn trajectories. Experiments on ALFWorld and WebShop show that GAGPO outperforms strong reinforcement learning baselines. Further analyses demonstrate faster early-stage learning, improved interaction efficiency, and smoother optimization dynamics, suggesting that GAGPO offers a simple yet effective framework for multi-turn agentic reinforcement learning.

A commonly accepted explanation of critic-free RL for LLMs, based on sequence-level rewards, is that it reinforces successful rollouts with a positive advantage while penalizing failed ones. In contrast, we study critic-free RL from a token-level perspective, revealing the token-flipping phenomenon: positive and negative rollouts exhibit remarkably similar proportions of tokens whose probabilities are boosted or suppressed during RL training. To explain this phenomenon, we further show that a token's change in probability is not fully determined by its own advantage; coupled gradient interactions with other tokens also play a non-negligible role. Specifically, these token coupling effects occur primarily between identical tokens that are both predicted with low confidence. Building upon this analysis, we propose the cancellation hypothesis: as a result of coupling, opposing signals cancel out for tokens shared by positive and negative rollouts, while tokens more specific to successful rollouts receive stronger reinforcement, thereby inducing hidden token-level credit assignment from rollout-level rewards. We support this hypothesis with complementary empirical evidence. (1) Compared with training on only positive rollouts, critic-free RL shifts updates from template and formatting tokens toward reasoning tokens; (2) Tokens boosted by critic-free RL consistently demonstrate higher value than suppressed tokens, regardless of whether they originate from positive or negative rollouts. Guided by this view, we implement two batching interventions to encourage or preserve cancellation in critic-free RL training: query-preserved mini-batching and reward-balanced batching. Despite their simplicity, these interventions improve RLVR training across multiple model scales, supporting cancellation as both an explanatory principle and a practical design criterion for critic-free RL training.

Reinforcement learning (RL) from unit-test feedback has become a standard post-training recipe for improving large language models (LLMs) on code generation. However, the pass-all-tests binary reward can be sparse, yielding no learning signal on challenging problems where none of the sampled solutions passes all tests. A common remedy is to use the test-case pass rate as a surrogate reward. In this work, we study pass-rate rewards in critic-free RL for code generation (e.g., GRPO and RLOO) and report a consistent pattern across base models and algorithms: despite alleviating reward sparsity, pass-rate rewards do not reliably improve final performance over binary rewards in rigorous controlled experiments. To understand this discrepancy, we analyze reward density and the resulting gradient directions. We find that pass-rate rewards are denser, but the induced gradient updates do not consistently move probability mass toward full-pass solutions. This arises because test-case pass rate is a miscalibrated surrogate for progress toward full correctness, and partial-pass solutions within the same group can induce conflicting gradient directions that cancel out. Overall, our results suggest that, in critic-free RL, pass-rate rewards are insufficient to improve code generation and motivate reward designs that better align optimization with the goal of full correctness.

Group Relative Policy Optimization (GRPO) remains the dominant critic-free approach for fine-tuning LLMs and VLMs, but its compatibility with constrained policy optimization (e.g. for safety-critical domains) has not been carefully examined. In this work, we introduce Constrained GRPO, a Lagrangian-based extension of GRPO for constrained policy optimization. We show that the standard practice of scalarizing rewards before normalization introduces a critical Lagrangian-specific failure mode: GRPO's within-group normalization makes constrained optimization highly sensitive to how multi-component learning signals are aggregated. We show that scalarizing rewards before normalization introduces shared-denominator coupling, so that changing one multiplier alters not only the emphasis on its corresponding constraint, but also the relative weighting of the reward and other constraints. We address this with a simple but crucial modification: scalarizing standardized advantages rather than rewards. This yields a better-conditioned update by addressing the coupling induced by reward scalarization, resulting in better-behaved multiplier dynamics and more stable constraint enforcement in practice. Empirically, across a controlled gridworld, a real-world autonomous driving benchmark, and a mathematical reasoning task, Constrained GRPO consistently achieves better adherence to specified constraints while maintaining or improving task performance.