Paper 2603.04918
BandPO: Bridging Trust Regions and Ratio Clipping via Probability-Aware Bounds for LLM Reinforcement Learning
- Published
- Mar 2026
- Research lab
- Independent
- Citations
- 2
- GitHub
- 49 stars
01 In brief
Summary
The paper introduces BandPO, a method for LLM reinforcement learning that replaces the fixed clipping bounds of PPO/GRPO with dynamic, probability-aware bounds derived from f-divergence trust regions.
The authors identify a bottleneck in canonical clipping: fixed bounds limit the upward update margin for low-probability actions, suppressing high-advantage tail strategies and causing entropy collapse.
BandPO projects trust regions into clipping intervals via a convex optimization problem, with closed-form solutions for TV and chi-squared divergences.
Experiments on Qwen2.5 (3B, 7B) and Llama3 (8B) show consistent improvements over GRPO and Clip-Higher on math benchmarks, with reduced entropy collapse.
The method uses a single interpretable radius parameter (delta) and is robust across model scales.
02 From the paper
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.