BAPO: Stabilizing Off-Policy Reinforcement Learning for LLMs via
  Balanced Policy Optimization with Adaptive Clipping
Authors: name: Zhiheng Xi, name: Xin Guo, name: Yang Nan, name: Enyu Zhou, name: Junrui Shen, name: Wenxiang Chen, name: Jiaqi Liu, name: Jixuan Huang, name: Zhihao Zhang, name: Honglin Guo, name: Xun Deng, name: Zhikai Lei, name: Miao Zheng, name: Guoteng Wang, name: Shuo Zhang, name: Peng Sun, name: Rui Zheng, name: Hang Yan, name: Tao Gui, name: Qi Zhang, name: Xuanjing Huang
Organization: Nex AGI

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.