Heterogeneous Adaptive Policy Optimization: Tailoring Optimization to Every Token’s Nature

AbstractUsing entropy as a measure of heterogeneity to guide optimization has emerged as a crucial research direction in Reinforcement Learning for LLMs. However, existing methods typically treat it as a discrete filter or post-hoc regulator rather than a core optimization driver. To fully leverage the potential of entropy and achieve fine-grained regulation, we introduce **H**eterogeneous **A**daptive **P**olicy **O**ptimization (HAPO), a token-aware algorithm that continuously adapts optimization dynamics based on token-level entropy throughout the entire training process. Our algorithm includes four key components: (1) **Adaptive Temperature Sampling** that adjusts sampling temperature in real time, promoting exploration at high-entropy tokens. (2) **Token-Level Group Average Advantage Estimation** that estimates advantages at token level, accounting for sequence-length effects while preserving non-biased treatment.(3) **Differential Advantage Redistribution** that leverages entropy and importance ratios to adjust advantages for tokens with clear signals. (4) **Asymmetric Adaptive Clipping** that dynamically adjusts clipping boundaries based on token-level entropy. Through systematic investigation of entropy, we embed token-level treatment into every stage. Extensive experiments on mathematical reasoning, code, and logic tasks across multiple models demonstrate HAPO’s consistent superiority over DAPO.