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

Yuan Li, Bo Wang, Yufei Gao, Yao Yuqian, Xinyuan Wang, Zhangyue Yin, Xipeng Qiu
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:70671-70692, 2026.

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. Code is publicly available at https://github.com/OpenMOSS/BandPO.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-li26gm, title = {{B}and{PO}: Bridging Trust Regions and Ratio Clipping via Probability-Aware Bounds for {LLM} Reinforcement Learning}, author = {Li, Yuan and Wang, Bo and Gao, Yufei and Yuqian, Yao and Wang, Xinyuan and Yin, Zhangyue and Qiu, Xipeng}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {70671--70692}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/li26gm/li26gm.pdf}, url = {https://proceedings.mlr.press/v306/li26gm.html}, 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. Code is publicly available at https://github.com/OpenMOSS/BandPO.} }
Endnote
%0 Conference Paper %T BandPO: Bridging Trust Regions and Ratio Clipping via Probability-Aware Bounds for LLM Reinforcement Learning %A Yuan Li %A Bo Wang %A Yufei Gao %A Yao Yuqian %A Xinyuan Wang %A Zhangyue Yin %A Xipeng Qiu %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-li26gm %I PMLR %P 70671--70692 %U https://proceedings.mlr.press/v306/li26gm.html %V 306 %X 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.
APA
Li, Y., Wang, B., Gao, Y., Yuqian, Y., Wang, X., Yin, Z. & Qiu, X.. (2026). BandPO: Bridging Trust Regions and Ratio Clipping via Probability-Aware Bounds for LLM Reinforcement Learning. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:70671-70692 Available from https://proceedings.mlr.press/v306/li26gm.html.

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