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$\xi$-DPO: Direct Preference Optimization via Ratio Reward Margin

Summary

ξ-DPO proposes a novel direct preference optimization method that addresses the joint hyperparameter tuning issue in SimPO by introducing a ratio reward margin (ξ). The method redefines rewards to yield a bounded and interpretable margin that can be derived from the initial reward distribution, eliminating trial-and-error tuning.

SourcearXiv Machine LearningAuthor: Zhengyuan Fan, Zhonghua Wu, Yuxuan Du, Qun Chen
$\xi$-DPO: Direct Preference Optimization via Ratio Reward Margin
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[2605.10981] $ξ$-DPO: Direct Preference Optimization via Ratio Reward Margin

[Submitted on 9 May 2026]

Title:$ξ$-DPO: Direct Preference Optimization via Ratio Reward Margin

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Abstract:Reference-free preference optimization has emerged as an efficient alternative to reinforcement learning from human feedback, with Simple Preference Optimization(SimPO) demonstrating strong performance by eliminating the explicit reference model through a simple objective. However, the joint tuning of the hyperparameters $\beta$ and $\gamma$ in SimPO remains a central challenge. We argue that this difficulty arises because the margin formulation in SimPO is not easily interpretable across datasets with different reward gap structures. To better understand this issue, we conduct a comprehensive analysis of SimPO and find that $\beta$ implicitly controls sample filtering, while the effect of $\gamma$ depends on the reward gap structure of the dataset. Motivated by these observations, we propose $\xi$-DPO: Direct preference optimization via ratio reward margin. We first reformulate the preference objective through an equivalent transformation, changing the optimization target from maximizing the likelihood of reward gaps to minimizing the distance between reward gaps and optimal margins. Then, we redefine the reward in a ratio form between the chosen and rejected, which effectively cancels the effect of $\beta$ and yields a bounded and interpretable margin. This margin is called the ratio reward margin and is denoted by $\xi$. Unlike the margin $\gamma$ in SimPO, $\xi$ explicitly represents the desired relative separation between chosen and rejected responses and can be determined from the initial reward gap distribution, avoiding repeated trial-and-error tuning. ....

Subjects:

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

Cite as: arXiv:2605.10981 [cs.LG]

(or arXiv:2605.10981v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2605.10981

arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Zhengyuan Fan [view email] [v1] Sat, 9 May 2026 03:48:16 UTC (361 KB)

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Key points and analysis

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Key points

  • SimPO eliminates reference model but faces difficulty in tuning hyperparameters β and γ due to uninterpretable margin across datasets.
  • Analysis reveals β implicitly controls sample filtering, while γ's effect depends on reward gap structure.
  • ξ-DPO transforms the objective from maximizing reward gap likelihood to minimizing distance between reward gap and optimal margin.
  • The ratio reward margin ξ is bounded, interpretable, and directly determined from initial reward distribution.

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