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 $π$PPO, a self-privileged actor-critic framework. By reusing verified same-prompt rollouts as contrastive evidence, $π$PPO helps the critic assess intermediate reasoning against successful and failed attempts, while preserving standard policy optimization and the deployment interface. Experiments show that $π$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.
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Cite this article
APA 7
Liang, K., Tang, C., Bai, C., Liu, W., Liu, Z., Zhang, Q., Yang, S., & Wu, Y. (2026). Privy to the Foil: Recasting Value Estimation with a Self-Privileged Critic for RLVR. https://omanscience.com/en/articles/privy-to-the-foil-recasting-value-estimation-with-a-self-privileged-critic-for-rlvr
MLA 9
Liang, Kun, et al. "Privy to the Foil: Recasting Value Estimation with a Self-Privileged Critic for RLVR." https://omanscience.com/en/articles/privy-to-the-foil-recasting-value-estimation-with-a-self-privileged-critic-for-rlvr.
Chicago (author–date)
Liang, Kun, Chenming Tang, Clive Bai, Weijie Liu, Zeyuan Liu, Qingyang Zhang, Saiyong Yang, and Yunfang Wu. 2026. "Privy to the Foil: Recasting Value Estimation with a Self-Privileged Critic for RLVR." https://omanscience.com/en/articles/privy-to-the-foil-recasting-value-estimation-with-a-self-privileged-critic-for-rlvr.
Harvard
Liang, K., Tang, C., Bai, C., Liu, W., Liu, Z., Zhang, Q., Yang, S. and Wu, Y. (2026) 'Privy to the Foil: Recasting Value Estimation with a Self-Privileged Critic for RLVR', Available at: https://omanscience.com/en/articles/privy-to-the-foil-recasting-value-estimation-with-a-self-privileged-critic-for-rlvr.
Vancouver
Liang K, Tang C, Bai C, Liu W, Liu Z, Zhang Q, et al. Privy to the Foil: Recasting Value Estimation with a Self-Privileged Critic for RLVR. https://omanscience.com/en/articles/privy-to-the-foil-recasting-value-estimation-with-a-self-privileged-critic-for-rlvr
IEEE
K. Liang, C. Tang, C. Bai, W. Liu, Z. Liu, Q. Zhang, S. Yang, and Y. Wu, "Privy to the Foil: Recasting Value Estimation with a Self-Privileged Critic for RLVR," https://omanscience.com/en/articles/privy-to-the-foil-recasting-value-estimation-with-a-self-privileged-critic-for-rlvr.