BandPO: Bridging Trust Regions and Ratio Clipping via Probability-Aware Bounds for LLM Reinforcement Learning

Proximal constraints are fundamental to the stability of the Large Language Model reinforcement learning. While the canonical clipping mechanism in PPO serves as an efficient surrogate for trust regions, we identify a critical bottleneck: fixed bounds strictly constrain the upward update margin of low-probability actions, disproportionately suppressing high-advantage tail strategies and inducing rapid entropy collapse. To address this, we introduce **Band-constrained Policy Optimization** (BandPO). BandPO replaces canonical clipping with **Band**, a unified theoretical operator that projects trust regions defined by $f$-divergences into dynamic, probability-aware clipping intervals. Theoretical analysis confirms that Band effectively resolves this exploration bottleneck. We formulate this mapping as a convex optimization problem, guaranteeing a globally optimal numerical solution while deriving closed-form solutions for specific divergences. Extensive experiments across diverse models and datasets demonstrate that BandPO consistently outperforms canonical clipping and Clip-Higher, while robustly mitigating entropy collapse. Code is publicly available at https://github.com/OpenMOSS/BandPO.

Large language models are often improved by letting them try different answers and rewarding the ones that work well. However, this training process must be carefully controlled: if the model changes too quickly, training can become unstable, but if it is controlled too rigidly, the model may stop exploring useful but initially unlikely answers. This paper identifies a limitation in a widely used control rule: it can overly restrict rare but promising choices, causing the model to become less diverse too quickly. We propose BandPO, a new training method that adjusts these control limits according to how likely each choice already is. This gives the model more room to learn from promising low-probability choices while still keeping training stable. Experiments on different models and datasets show that BandPO improves performance over existing methods and helps prevent the model from losing useful diversity during training.