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

TL;DR

BandPO introduces a probability-aware clipping method for LLM reinforcement learning that overcomes the limitations of fixed bounds, enhancing exploration and stability.

Contribution

It proposes a novel operator, Band, that dynamically adjusts trust region bounds based on probability, improving upon canonical clipping in PPO.

Findings

Outperforms canonical clipping and Clip-Higher in experiments

Mitigates entropy collapse effectively

Enhances exploration in LLM RL tasks

Abstract

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.