Junrui Shen

Jiazheng Zhang, Ziche Fu, Junrui Shen et al.

Policy entropy has emerged as a fundamental measure for understanding and controlling exploration in reinforcement learning with verifiable rewards (RLVR) for LLMs. However, existing entropy-aware methods mainly regulate entropy through global objectives, while the token-level mechanism by which sampled policy updates reshape policy entropy remains underexplored. In this work, we develop a theoretical framework of entropy mechanics in RLVR. Our analysis yields a first-order approximation of the entropy change, giving rise to entropy polarity, a signed token-level quantity that predicts how much a sampled update expands or contracts entropy. This analysis further reveals a structural asymmetry: reinforcing frequent high-probability tokens triggers contraction tendencies, whereas expansive tendencies typically require lower-probability samples or stronger distributional correction. Empirically, we show that entropy polarity reliably predicts entropy changes, and that positive and negative polarity branches play complementary roles in preserving exploration while strengthening exploitation. Building on these insights, we propose Polarity-Aware Policy Optimization (PAPO), which preserves both polarity branches and implements entropy control through advantage reweighting. With the empirical entropy trajectory as an online phase signal, PAPO adaptively reallocates optimization pressure between entropy-expanding and entropy-contracting updates. Experiments on mathematical reasoning and agentic benchmarks show that PAPO consistently outperforms competitive baselines, while delivering superior training efficiency and substantial reward improvements.

Zhiheng Xi, Xin Guo, Yang Nan et al.

Reinforcement learning (RL) has recently become the core paradigm for aligning and strengthening large language models (LLMs). Yet, applying RL in off-policy settings--where stale data from past policies are used for training--improves sample efficiency, but remains challenging: policy entropy declines sharply, optimization often becomes unstable and may even collapse. Through theoretical and empirical analysis, we identify two key insights: (i) an imbalance in optimization, where negative-advantage samples dominate the policy gradient, suppressing useful behaviors and risking gradient explosions; and (ii) the derived Entropy-Clip Rule, which reveals that the fixed clipping mechanism in PPO-like objectives systematically blocks entropy-increasing updates, thereby driving the policy toward over-exploitation at the expense of exploration. Building on these insights, we propose BAlanced Policy Optimization with Adaptive Clipping (BAPO), a simple yet effective method that dynamically adjusts clipping bounds to adaptively re-balance positive and negative contributions, preserve entropy, and stabilize RL optimization. Across diverse off-policy scenarios--including sample replay and partial rollout--BAPO achieves fast, stable, and data-efficient training. On AIME 2024 and AIME 2025 benchmarks, our 7B BAPO model surpasses open-source counterparts such as SkyWork-OR1-7B, while our 32B BAPO model not only achieves state-of-the-art results among models of the same scale but also outperforms leading proprietary systems like o3-mini and Gemini-2.5-Flash-Thinking.