Privy to the Foil: Recasting Value Estimation with a Self-Privileged Critic for RLVR

arXiv:2609.37825v1 Announce Type: new Abstract: Assigning credit to intermediate steps remains a central challenge in training Large Language Models (LLMs) on multi-step reasoning tasks with sparse terminal rewards, and actor-critic methods such as PPO address this by learning value functions to construct token-level advantages. Their effectiveness, however, hinges on reliable value estimation, a difficult task requiring the critic to both assess progress toward a correct solution and anticipate an evolving policy's future behavior; errors in either can compromise credit assignment and destabilize online training. In this paper, we revisit the standard state-only formulation of value estimation and propose $\pi$PPO, a self-privileged actor-critic framework. By reusing verified same-prompt rollouts as contrastive evidence, $\pi$PPO helps the critic assess intermediate reasoning against successful and failed attempts, while preserving standard policy optimization and the deployment interface. Experiments show that $\pi$PPO consistently improves value-estimation quality by a substantial margin and outperforms representative actor-critic and critic-free RLVR baselines on challenging mathematical reasoning benchmarks, while remaining effective even when paired with substantially smaller asymmetric critics.

Abstract:Assigning credit to intermediate steps remains a central challenge in training Large Language Models (LLMs) on multi-step reasoning tasks with sparse terminal rewards, and actor-critic methods such as PPO address this by learning value functions to construct token-level advantages. Their effectiveness, however, hinges on reliable value estimation, a difficult task requiring the critic to both assess progress toward a correct solution and anticipate an evolving policy's future behavior; errors in either can compromise credit assignment and destabilize online training. In this paper, we revisit the standard state-only formulation of value estimation and propose $\pi$PPO, a self-privileged actor-critic framework. By reusing verified same-prompt rollouts as contrastive evidence, $\pi$PPO helps the critic assess intermediate reasoning against successful and failed attempts, while preserving standard policy optimization and the deployment interface. Experiments show that $\pi$PPO consistently improves value-estimation quality by a substantial margin and outperforms representative actor-critic and critic-free RLVR baselines on challenging mathematical reasoning benchmarks, while remaining effective even when paired with substantially smaller asymmetric critics.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2609.37825 [cs.LG]

(or arXiv:2609.37825v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.37825 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Privy to the Foil: Recasting Value Estimation with a Self-Privileged Critic for RLVR

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