@inproceedings{zhang-etal-2026-freemu,
title = "{F}ree{MU}: Free Marginal Utility for Reward-Aware Direct Preference Optimization",
author = "Zhang, Lei and
Ma, Jian and
Zhang, Xianpeng and
Chen, Dongyu and
Lu, Haonan and
Su, Tianhuang and
Wang, Chuangchuang and
Tang, Kai and
Su, Zhixun",
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.1871/",
pages = "39932--39953",
ISBN = "979-8-89176-462-0",
abstract = "Reward-aware variants of Direct Preference Optimization (DPO), such as ODPO and MODPO, implicitly assume linear marginal utility over the preference signal: identical signal gaps induce identical gradient updates regardless of whether the pair lies in a low- or high-quality region. We propose FreeMU, a lightweight plug-and-play training module that introduces non-linear marginal utility through a pair-aware divided-difference weight applied directly to the preference margin. The same weight formula integrates with three representative DPO variants{---}ODPO, MODPO, and {\ensuremath{\beta}}-DPO{---}with each instantiation differing only in the reward source and its normalisation. We first instantiate FreeMU on the two explicit-score variants (Likert labels for ODPO and reward-model outputs for MODPO) and then, for variants without externally annotated scores, on {\ensuremath{\beta}}-DPO using the implicit Bradley{--}Terry reward induced by the policy and reference models. Across summarization, multi-objective safety alignment, and dialogue, FreeMU consistently improves over its host in LLM-based win rates and task-specific metrics with near-zero training overhead; a controlled ablation confirms that the convex curvature direction is the operative ingredient{---}reversing the sign to a concave utility removes the gain."
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<abstract>Reward-aware variants of Direct Preference Optimization (DPO), such as ODPO and MODPO, implicitly assume linear marginal utility over the preference signal: identical signal gaps induce identical gradient updates regardless of whether the pair lies in a low- or high-quality region. We propose FreeMU, a lightweight plug-and-play training module that introduces non-linear marginal utility through a pair-aware divided-difference weight applied directly to the preference margin. The same weight formula integrates with three representative DPO variants—ODPO, MODPO, and \ensuremathβ-DPO—with each instantiation differing only in the reward source and its normalisation. We first instantiate FreeMU on the two explicit-score variants (Likert labels for ODPO and reward-model outputs for MODPO) and then, for variants without externally annotated scores, on \ensuremathβ-DPO using the implicit Bradley–Terry reward induced by the policy and reference models. Across summarization, multi-objective safety alignment, and dialogue, FreeMU consistently improves over its host in LLM-based win rates and task-specific metrics with near-zero training overhead; a controlled ablation confirms that the convex curvature direction is the operative ingredient—reversing the sign to a concave utility removes the gain.</abstract>
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%0 Conference Proceedings
%T FreeMU: Free Marginal Utility for Reward-Aware Direct Preference Optimization
%A Zhang, Lei
%A Ma, Jian
%A Zhang, Xianpeng
%A Chen, Dongyu
%A Lu, Haonan
%A Su, Tianhuang
%A Wang, Chuangchuang
%A Tang, Kai
%A Su, Zhixun
%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 zhang-etal-2026-freemu
%X Reward-aware variants of Direct Preference Optimization (DPO), such as ODPO and MODPO, implicitly assume linear marginal utility over the preference signal: identical signal gaps induce identical gradient updates regardless of whether the pair lies in a low- or high-quality region. We propose FreeMU, a lightweight plug-and-play training module that introduces non-linear marginal utility through a pair-aware divided-difference weight applied directly to the preference margin. The same weight formula integrates with three representative DPO variants—ODPO, MODPO, and \ensuremathβ-DPO—with each instantiation differing only in the reward source and its normalisation. We first instantiate FreeMU on the two explicit-score variants (Likert labels for ODPO and reward-model outputs for MODPO) and then, for variants without externally annotated scores, on \ensuremathβ-DPO using the implicit Bradley–Terry reward induced by the policy and reference models. Across summarization, multi-objective safety alignment, and dialogue, FreeMU consistently improves over its host in LLM-based win rates and task-specific metrics with near-zero training overhead; a controlled ablation confirms that the convex curvature direction is the operative ingredient—reversing the sign to a concave utility removes the gain.
%U https://aclanthology.org/2026.findings-emnlp.1871/
%P 39932-39953
Markdown (Informal)
[FreeMU: Free Marginal Utility for Reward-Aware Direct Preference Optimization](https://aclanthology.org/2026.findings-emnlp.1871/) (Zhang et al., Findings 2026)
ACL
- Lei Zhang, Jian Ma, Xianpeng Zhang, Dongyu Chen, Haonan Lu, Tianhuang Su, Chuangchuang Wang, Kai Tang, and Zhixun Su. 2026. FreeMU: Free Marginal Utility for Reward-Aware Direct Preference Optimization. In Findings of the Association for Computational Linguistics: EMNLP 2026, pages 39932–39953, Budapest, Hungary. Association for Computational Linguistics.