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This paper introduces Advantage-Based Control Variates (ABC), a novel actor-critic framework designed to reduce bias in reinforcement learning with verifiable rewards by leveraging trajectory-level control variates. The method demonstrates that ABC can match the performance of critic-free approaches like GRPO while requiring fewer online optimization steps, particularly on mathematical reasoning tasks. By combining ABC with Direct Advantage Estimation, the authors propose a more efficient algorithm for adapting to offline-to-online learning settings.
ABC: Advantage-Based Control Variates for Reinforcement Learning with Verifiable Rewards
arXiv:2609.36058v1 Announce Type: new Abstract: Recent progress in reinforcement learning with verifiable rewards (RLVR) has highlighted the effectiveness of simple critic-free policy-gradient methods such as Group Relative Policy Optimization (GRPO). In contrast, actor-critic methods rely on learned value functions whose approximation error can introduce bias through commonly used advantage estimators such as temporal-difference error. Motivated by this observation, we revisit trajectory-level control variates through an advantage-value formulation, which we call Advantage-Based Control Variates (ABC). This formulation reveals that the covariance structure is closely related to the return decomposition used in Direct Advantage Estimation (DAE). Finally, we combine ABC with DAE into a single actor-critic algorithm and evaluate it in an offline-to-online RLVR setting, where the critic is first trained on previously collected trajectories and adapted during online learning. On mathematical reasoning tasks, ABC achieves performance competitive with GRPO using substantially fewer online optimization steps.
Abstract:Recent progress in reinforcement learning with verifiable rewards (RLVR) has highlighted the effectiveness of simple critic-free policy-gradient methods such as Group Relative Policy Optimization (GRPO). In contrast, actor-critic methods rely on learned value functions whose approximation error can introduce bias through commonly used advantage estimators such as temporal-difference error. Motivated by this observation, we revisit trajectory-level control variates through an advantage-value formulation, which we call Advantage-Based Control Variates (ABC). This formulation reveals that the covariance structure is closely related to the return decomposition used in Direct Advantage Estimation (DAE). Finally, we combine ABC with DAE into a single actor-critic algorithm and evaluate it in an offline-to-online RLVR setting, where the critic is first trained on previously collected trajectories and adapted during online learning. On mathematical reasoning tasks, ABC achieves performance competitive with GRPO using substantially fewer online optimization steps.
Machine Learning (cs.LG)
arXiv:2609.36058 [cs.LG]
(or arXiv:2609.36058v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.36058 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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