Advantage Shaping as Surrogate Reward Maximization: Unifying Pass@K Policy Gradients

Christos Thrampoulidis; Sadegh Mahdavi; Wenlong Deng

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arXiv · 2510.23049

Advantage Shaping as Surrogate Reward Maximization: Unifying Pass@K Policy Gradients

Christos Thrampoulidis·Sadegh Mahdavi·Wenlong Deng

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Abstract

This note reconciles two seemingly distinct approaches to policy gradient optimization for the Pass@K objective in reinforcement learning with verifiable rewards: (1) direct REINFORCE-style methods, and (2) advantage-shaping techniques that directly modify GRPO. We show that these are two sides of the same coin. By reverse-engineering existing advantage-shaping algorithms, we reveal that they implicitly optimize surrogate rewards. We specifically interpret practical "hard-example up-weighting" modifications to GRPO as reward-level regularization. Conversely, starting from surrogate reward objectives, we provide a simple recipe for deriving both existing and new advantage-shaping methods. This perspective provides a lens for RLVR policy gradient optimization beyond our original motivation of Pass@K.

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Christos Thrampoulidis, Sadegh Mahdavi, Wenlong Deng. 2025-10-27. Advantage Shaping as Surrogate Reward Maximization: Unifying Pass@K Policy Gradients. https://arxiv.org/abs/2510.23049

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