Spurious Advantage Hidden in GRPO

Group Relative Policy Optimization (GRPO) is widely studied for reinforcement learning with verifiable rewards, where its advantage estimator assigns each rollout a magnitude from within-group reward statistics. In the common case, this magnitude rewards rollouts that reach the correct answer through reasoning. Yet, an overlooked case shares the same surface: a rollout may land on it by guessing, and the formula still assigns a high magnitude, which we identify as the spurious advantage. This arises in three cases: bounded-answer tasks with a small candidate set; open-answer sets hosting bounded sub-cases; and search agents whose budget opens many paths to the same answer. In all three, this misleads the policy toward guess-like behaviors. We propose SIGNBALANCE, whose magnitude is composition-free: it keeps the verifier sign, uses a global scale, and restores zero-mean balance via a stop-gradient per-class rescaling. Across math and search agent benchmarks at different scales, SIGNBALANCE matches GRPO on open-answer math and improves on bounded-answer math and search agents. Code will be released.

How to Train a Critic Stably and Efficiently

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 \textbf{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

Annotations as Rollouts: Efficient and Scalable Reinforcement Learning for Video MLLMs

Multimodal large language models (MLLMs) have become a prevailing paradigm for unified video perception. However, post-training on large multi-task datasets remains challenging, as existing reinforcement learning methods sample on-policy groups with few high-quality rollouts even with costly chain-of-thought (CoT) generation. In this paper, we study the sample efficiency and scalability of RL post-training for video MLLMs and introduce OraRL. We identify an overlooked role for annotations: Beyond scoring rollouts, each can enter its on-policy group as an oracle rollout, a direct positive optimization target. Direct oracle integration, however, is nontrivial: a high-reward oracle raises the group baseline and inverts otherwise positive policy advantages, a failure we term advantage inversion. At the core of OraRL is a decoupled advantage estimator: policy rollouts determine an oracle-free baseline, while the oracle-policy gap modulates both a directional gain and a separate detached oracle advantage. Sign-balanced pruning improves efficiency: by retaining only the oracle and the strongest rollouts of each sign, OraRL requires just 2.2x the step time of SFT, less than half the 4.9x required by GRPO with CoT. OraRL scales with model size and data, surpassing its backbone from 0.8B to 9B and GRPO up to 100k prompts. Without chain-of-thought, Video-ORA-9B decodes in 130 ms instead of 4,780 ms. Compared with the respective prior best models, it raises temporal mIoU from 62.5 to 66.0, tracking AO from 73.0 to 78.2, segmentation from 64.3 to 70.4, and the three-benchmark spatial-intelligence macro average from 51.0 to 56.1; on VSI-Bench, it scores 73.1 against 55.0 for GPT-5 and 55.1 for Gemini-3-Pro.

SAPO: Single-Rollout Autoregressive Policy Optimization for Agentic Reinforcement Learning

Agentic reinforcement learning (RL) has become a critical stage in the post-training of large language models. Existing critic-free, group-relative methods estimate policy advantages from multiple rollouts, avoiding the substantial memory overhead of conventional proximal policy optimization (PPO) and achieving strong performance on long-horizon interactive tasks. Despite their success, recent studies revealed three limitations: (1) Lack explicit value generalization and effective temporal credit assignment; (2) Suffer from potential advantage collapse in long-horizon complex tasks; (3) Require a costly trade-off between sampling budget and policy performance. In this work, we propose Single-rollout Autoregressive Policy Optimization (SAPO), a low-memory and compute-efficient framework in which the policy and value functions share a single autoregressive backbone. SAPO exploits the autoregressive structure of LLMs to produce policy and value predictions at distinct causal boundaries with shared parameters, while independently optimizing the PPO objectives and auxiliary on-policy SARSA objectives. To robustly estimate the contribution of each turn, we further introduce a trajectory-level generalized advantage estimator that combines lambda-returns with batch normalization. Experiments across ALFWorld and WebShop with Qwen2.5-1.5B/7B show that SAPO trains stably and outperforms PPO and GRPO by mean +15.1 and +12.1 percentage points, respectively, while eliminating the memory cost of a separate critic model and reducing per-iteration runtime by 33.2% over PPO.

PlanPO: Group Planning-Aware Policy Optimization for Multi-Turn Agentic LLMs

Group-relative policy optimization has emerged as a key paradigm for training agentic large language models (LLMs) on multi-turn interactive tasks. However, most existing variants fail to distinguish advantages among successful trajectories even when these trajectories differ substantially in their interaction efficiency. For instance, circuitous successes are often assigned the identical outcome reward, causing advantage collapse and severe performance bottlenecks. To this end, we propose Group Planning-aware Policy Optimization (PlanPO), a simple yet effective RL method for learning generalizable planning abilities beyond task-specific high-quality behavior patterns. Specifically, PlanPO introduces coarse-to-fine advantage signals, which capture the relative differences in trajectory-level lengths and turn-level response lengths conditioned on successful trajectories sampled for the same task. Within the group-relative optimization structure, this enables agents to actively learn generalizable and deliberate behaviors spanning interaction planning and textual generation from high-quality rollouts, without degenerating into vanilla length minimization. Experimentally, PlanPO improves over GRPO by 27.2\% on average across the challenging multi-turn benchmarks ALFWorld, WebShop, and SciWorld, outperforming recent powerful baselines while incurring negligible additional training cost.

Gated-BEPO: Confidence-Gated Bellman Credit Assignment for Large Language Model Agents

Training large language model agents in long-horizon environments requires assigning credit from sparse terminal outcomes to individual actions. Existing critic-free methods propagate trajectory-level rewards uniformly across steps, while recent approaches construct step-level groups by matching repeated states and compare actions within each group. The former cannot distinguish useful actions in failed trajectories from ineffective actions in successful ones. The latter rely on step credit derived directly from individual trajectory outcomes and fixed-weight fusion with episode-level credit. We propose Gated-BEPO, which derives step-level credit from empirical rollout graphs. For each rollout group, Gated-BEPO constructs an empirical graph and estimates node values through a mean-backup Bellman fixed point that reflects the empirical action distribution of the current policy. We then accumulate these temporal-difference residuals along each sampled trajectory using generalized advantage estimation, yielding step-level Bellman advantages that capture both immediate and downstream effects. To adaptively fuse episode- and step-level credit, a confidence gate incorporates Bellman credit only at states with multiple observed successors and otherwise uses episode-level credit. Experiments on WebShop, ALFWorld, and visual Sokoban show consistent improvements across language and vision-language models, while diagnostic ablations support the effectiveness of Bellman fixed-point value estimation and show that step-level credit should be incorporated selectively rather than uniformly into the final advantage.

Hybrid Advantage Estimation with Unified Critic for VLM Agentic Reinforcement Learning

Large Vision-Language Models (VLMs) now act as agents in interactive environments, where success requires coherent reasoning and decision-making across turns. Although end-to-end training in agentic environments can improve such multi-turn decision-making abilities, current methods mainly rely on either token-wise optimization over concatenated token trajectories or turn-wise optimization with uniform within-turn credit. In this work, we establish theoretical formulations for the two levels of optimization and derive a hybrid advantage that serves both objectives. Furthermore, with an appropriate choice of discount factor and learning target, we prove that a unified critic model can estimate values for both turn-wise and token-wise. As such, we propose HyGAE, an actor-critic framework that jointly optimizes token- and turn-level objectives with the hybrid advantage and unified critic. We conduct extensive evaluations of HyGAE across five multi-turn decision-making environments, where it achieves an average success rate of 91% and a significant improvement of 10% over other methods. Furthermore, we provide an in-depth analysis showing that the exact analytic form of the hybrid advantage and return is crucial for optimization. Project Page: https://wx-zhang.github.io/hygae-web/.

Relative Value Learning

In reinforcement learning, critics typically estimate absolute state values $V(s)$, estimating how good a particular situation is in isolation. However, it turns out that only differences in value are relevant for control. Motivated by this, we propose Relative Value Learning (RV), a framework that learns value differences directly via an antisymmetric function $Δ(s_i, s_j) = V(s_i) - V(s_j)$. We introduce a pairwise Bellman operator and prove it is a $γ$-contraction with a unique fixed point equal to the true value differences, derive well-posed $1$-step, $n$-step and $λ$-return targets and reconstruct generalized advantage estimation from pairwise differences to obtain an unbiased policy-gradient estimator (R-GAE). Beyond theoretical results, we integrate RV with PPO and achieve competitive performance on the Atari benchmark (49 ALE games) compared to standard PPO, indicating that relative value estimation is an effective alternative to absolute critics.

BV-Blend: Uncertainty-Weighted Historical Baselines for Stable Critic-Free RL with Verifiable Rewards

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.

BiPACE: Bisimulation-Guided Policy Optimization with Action Counterfactual Estimation for LLM Agents

Stepwise group-based RL is an attractive way to train long-horizon LLM agents without a learned critic: it reuses multiple sampled rollouts to estimate local advantages. Its weakness is less visible but more fundamental: every group-relative estimator assumes that the steps it compares are equivalent for credit assignment. We show that current agentic variants violate this assumption through a state-action credit mismatch. The observation-hash partition is overly fine on the state side, creating singleton groups with zero step-level signal, while a single within-group mean is too coarse on the action side, mixing state-value estimation with action-specific credit. We introduce BiPACE (Bisimulation-Guided Policy Optimization with Action Counterfactual Estimation), a drop-in advantage estimator that fixes both sides without adding a critic, auxiliary loss, or extra rollouts. BiGPO clusters steps by cosine distance in the actor's own hidden-state geometry, an empirical policy-induced proxy for bisimulation that substantially lowers the singleton rate left by observation hashing. PACE then recenters returns within each behavioral cluster using action-conditioned peer baselines; its Q-style instance estimates a local Q(s,a)-V(s) nonparametrically. On ALFWorld/Qwen2.5-7B, BiPACE_Q raises overall validation success from GiGPO's 90.8 to $97.1\pm0.9$ over three seeds, and crosses the 95% threshold on every seed, which GiGPO never does within the same budget. On Qwen2.5-1.5B it reaches $93.5\pm1.2$ versus GiGPO's 86.7, and on WebShop and TextCraft it improves over GRPO and GiGPO at both model scales. The measured BiPACE-specific overhead is 11.3% of a single training-step wall time. Yet it changes the estimator's comparison unit from surface identity to approximate behavioral equivalence plus action-side counterfactuals. The code is available at https://github.com/TianxiangZhao/BiPACE.

Low Variance Trust Region Optimization with Independent Actors and Sequential Updates in Cooperative Multi-agent Reinforcement Learning

Cooperative multi-agent reinforcement learning assumes each agent shares the same reward function and can be trained effectively using the Trust Region framework of single-agent. Instead of relying on other agents' actions, the independent actors setting considers each agent to act based only on its local information, thus having more flexible applications. However, in the sequential update framework, it is required to re-estimate the joint advantage function after each individual agent's policy step. Despite the practical success of importance sampling, the updated advantage function suffers from exponentially high variance problems, which likely result in unstable convergence. In this work, we first analyze the high variance advantage both empirically and theoretically. To overcome this limitation, we introduce a clipping objective to control the upper bounds of the advantage fluctuation in sequential updates. With the proposed objective, we provide a monotonic bound with sub-linear convergence to $ε$-Nash Equilibria. We further derive two new practical algorithms using our clipping objective. The experiment results on three popular multi-agent reinforcement learning benchmarks show that our proposed method outperforms the tested baselines in most environments. By carefully analyzing different training settings, our proposed method is highlighted with both stable convergence properties and the desired low advantage variance estimation. For reproducibility purposes, our source code is publicly available at https://github.com/giangbang/Low-Variance-Trust-Region-MARL.

On the Variance of Temporal Difference Learning and its Reduction Using Control Variates

We analyze the variance of temporal difference (TD) learning using the phased setting with tabular representation, and show that one of the mechanisms behind its ability to reduce variance is by effectively aggregating over a larger number of independent trajectories. Based on this insight, we demonstrate that (1) the variance of TD is asymptotically bounded from above by Monte Carlo (MC) estimators, and (2) shorter horizon updates incurs less variance for a fixed number of samples. Beyond TD, we show that Direct Advantage Estimation (DAE), a method for estimating the advantage function, can be seen as a type of regression-adjusted control variate, which achieves a tighter bound on the variance compared to TD in the large-sample limit. Finally, we numerically illustrate the behaviors of these estimators with carefully designed environments.

Rethinking Groups in Critic-Free RLVR

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.

PAWS: Preference Learning with Advantage-Weighted Segments

Preference-based reinforcement learning (PbRL) learns policies from human trajectory-level comparisons, avoiding explicit reward design and expert demonstrations. Existing methods typically train utility functions on trajectory or segment-level preferences while relying on per-step utility estimates during policy optimization. This training and inference mismatch induces a distribution shift that severely degrades temporal credit assignment and limits policy learning. We analyze this issue and propose PAWS, a segment-based preference learning method that performs policy updates directly using segment-level advantage functions. By aligning utility training with policy optimization, PAWS preserves trajectory-level preference information and avoids unreliable per-step learning signals. Experiments on simulated robotic manipulation and locomotion tasks demonstrate that PAWS consistently outperforms existing PbRL approaches, highlighting the importance of distribution-consistent preference learning.

Representation-Aware Advantage Estimation: Your Reward Model Provides More Than A Scalar Output

Current reinforcement learning from human feedback (RLHF) methods primarily rely on scalar rewards from a trained reward model (RM). While effective, scalar rewards are often noisy and fail to capture fine-grained preference differences, whereas RM hidden states encode richer semantic and preference information. We introduce the representation-aware advantage estimation, which leverages RM hidden states and models them as auxiliary signals for better advantage estimation. Specifically, we propose the Graph-based Advantage Estimation (GraphAE), treat each sampled group as a graph, where nodes correspond to responses and edges capture their similarity in the RM hidden space. Then advantages are computed via graph propagation, enabling each sample to incorporate contextual information from its neighbors. GraphAE is lightweight and can be seamlessly integrated into existing group-based RL algorithms. We apply GraphAE to GRPO, GSPO and RLOO, and conduct extensive experiments on different models and benchmarks. Empirical results show consistent improvements across three benchmarks, with gains of up to + 6.3 on Arena-Hard-v0.1, + 8.27 on AlpacaEval 2.0, and + 0.22 on MT-Bench. These results demonstrate that leveraging RM representations leads to more sample efficient and robust RLHF.

AdaGRPO: A Capability-Aware Adaptive Enhancement for Flow-based GRPO

Group Relative Policy Optimization (GRPO) has demonstrated remarkable success in aligning text-to-image (T2I) flow models with human preferences. However, we have identified that the learning loop of current flow-based GRPO is fundamentally decoupled from the learner's current capability, suffering from critical blind spots at both prompt selection and advantage estimation: (i) Existing methods sample prompts randomly, overlooking the substantial impact of data selection on reinforcement learning (RL) efficacy--a factor proven crucial in GRPO for large language models; (ii) They evaluate sample quality solely relying on intra-group statistics, lacking a global perspective to accurately measure true policy improvement. To address these issues, we propose Adaptive GRPO (AdaGRPO), a novel capability-aware RL algorithm tailored for flow models. Specifically, AdaGRPO consists of two principal components: (i) Online Curriculum Filtering Strategy: Dynamically tracks the model's proficiency and adaptively selects prompts that best match its current learning boundary; (ii) Cross-Level Advantage Fusion: Synergistically integrates fine-grained intra-group advantages with macro-level global advantages, providing a comprehensive and unbiased policy evaluation. As a lightweight, plug-and-play module, AdaGRPO can be seamlessly integrated with existing frameworks such as Flow-GRPO, DanceGRPO, and Flow-CPS. Extensive experiments demonstrate that AdaGRPO consistently drives performance gains while significantly stabilizes GRPO training for flow models.

On Advantage Estimates for Max@K Policy Gradients

Reinforcement learning with verifiable rewards is widely used for post-training reasoning models, but sparse outcome rewards make exploration difficult. A complementary approach is to optimize inference-time objectives such as pass@K and max@K directly, yet existing policy-gradient estimators for these objectives use different signals, baselines, and normalizations, making their relationships unclear. We study this issue through baseline design and advantage centering. Starting from the advantage estimator of a leading method in the field, we show that it is policy-gradient unbiased but yields a non-centered advantage. We then introduce a Leave-Two-Out baseline that preserves policy-gradient unbiasedness while making realized batch advantages exactly centered. The resulting method, MaxPO, has an efficient quadratic-time implementation and integrates naturally into group-based RL for LLM post-training. We further derive the canonical finite-batch advantage for max@K, providing a unified view of existing advantage estimators. Empirically, we verify that the L2O baseline reduces gradient variance and outperforms non-centered alternatives.