@inproceedings{xiao-etal-2026-bnpo,
title = "{BNPO}: Beta Normalization Policy Optimization",
author = "Xiao, Changyi and
Zhang, Mengdi and
Cao, Yixin",
editor = "Lee, Hung-Yi and
Dev, Sunipa and
Li, Jessy and
Elliott, Desmond",
booktitle = "Findings of the {A}ssociation for {C}omputational {L}inguistics: {EMNLP} 2026",
month = oct,
year = "2026",
address = "Budapest, Hungary",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2026.findings-emnlp.2364/",
pages = "50817--50829",
ISBN = "979-8-89176-462-0",
abstract = "Reinforcement learning with rule-based, binary-valued reward functions has been shown to significantly enhance the reasoning capabilities of large language models. These models typically rely on REINFORCE-based policy optimization methods, such as REINFORCE with baseline and group relative policy optimization (GRPO). However, a key limitation is that existing methods either ignore reward normalization or use static normalization schemes, which fail to adapt to the evolving policy during training. This mismatch can lead to unstable gradient estimates and hinder training stability. To address this issue, we propose Beta Normalization Policy Optimization (BNPO), a novel method that adaptively normalizes rewards using a Beta distribution with dynamically updated parameters. By aligning normalization with the changing policy distribution, BNPO enables more accurate, lower-variance gradient estimation and promotes stable training dynamics. We provide theoretical analysis showing that BNPO reduces variance and generalizes both REINFORCE and GRPO under binary-valued rewards. In addition, we introduce an advantage decomposition mechanism to extend BNPO to more complex reward settings. Experimental results demonstrate that BNPO achieves state-of-the-art performance among policy optimization methods on reasoning tasks."
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<abstract>Reinforcement learning with rule-based, binary-valued reward functions has been shown to significantly enhance the reasoning capabilities of large language models. These models typically rely on REINFORCE-based policy optimization methods, such as REINFORCE with baseline and group relative policy optimization (GRPO). However, a key limitation is that existing methods either ignore reward normalization or use static normalization schemes, which fail to adapt to the evolving policy during training. This mismatch can lead to unstable gradient estimates and hinder training stability. To address this issue, we propose Beta Normalization Policy Optimization (BNPO), a novel method that adaptively normalizes rewards using a Beta distribution with dynamically updated parameters. By aligning normalization with the changing policy distribution, BNPO enables more accurate, lower-variance gradient estimation and promotes stable training dynamics. We provide theoretical analysis showing that BNPO reduces variance and generalizes both REINFORCE and GRPO under binary-valued rewards. In addition, we introduce an advantage decomposition mechanism to extend BNPO to more complex reward settings. Experimental results demonstrate that BNPO achieves state-of-the-art performance among policy optimization methods on reasoning tasks.</abstract>
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%0 Conference Proceedings
%T BNPO: Beta Normalization Policy Optimization
%A Xiao, Changyi
%A Zhang, Mengdi
%A Cao, Yixin
%Y Lee, Hung-Yi
%Y Dev, Sunipa
%Y Li, Jessy
%Y Elliott, Desmond
%S Findings of the Association for Computational Linguistics: EMNLP 2026
%D 2026
%8 October
%I Association for Computational Linguistics
%C Budapest, Hungary
%@ 979-8-89176-462-0
%F xiao-etal-2026-bnpo
%X Reinforcement learning with rule-based, binary-valued reward functions has been shown to significantly enhance the reasoning capabilities of large language models. These models typically rely on REINFORCE-based policy optimization methods, such as REINFORCE with baseline and group relative policy optimization (GRPO). However, a key limitation is that existing methods either ignore reward normalization or use static normalization schemes, which fail to adapt to the evolving policy during training. This mismatch can lead to unstable gradient estimates and hinder training stability. To address this issue, we propose Beta Normalization Policy Optimization (BNPO), a novel method that adaptively normalizes rewards using a Beta distribution with dynamically updated parameters. By aligning normalization with the changing policy distribution, BNPO enables more accurate, lower-variance gradient estimation and promotes stable training dynamics. We provide theoretical analysis showing that BNPO reduces variance and generalizes both REINFORCE and GRPO under binary-valued rewards. In addition, we introduce an advantage decomposition mechanism to extend BNPO to more complex reward settings. Experimental results demonstrate that BNPO achieves state-of-the-art performance among policy optimization methods on reasoning tasks.
%U https://aclanthology.org/2026.findings-emnlp.2364/
%P 50817-50829
Markdown (Informal)
[BNPO: Beta Normalization Policy Optimization](https://aclanthology.org/2026.findings-emnlp.2364/) (Xiao et al., Findings 2026)
ACL
- Changyi Xiao, Mengdi Zhang, and Yixin Cao. 2026. BNPO: Beta Normalization Policy Optimization. In Findings of the Association for Computational Linguistics: EMNLP 2026, pages 50817–50829, Budapest, Hungary. Association for Computational Linguistics.