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

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 β and γ 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 β, rather than merely serving as a reward scaling factor, primarily functions to filter noisy samples, while the reward margin γ defined by SimPO is not semantically well aligned with explicitly enlarging the reward gap between chosen and rejected responses. Motivated by these observations, we propose ξ-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 β and yields a bounded and interpretable margin. This margin is called the ratio reward margin and is denoted by ξ. Unlike the β and γ in SimPO, ξ can be determined from the initial reward gap distribution, thus much easier to tune. Our extensive experimental results show that ξ-DPO substantially outperforms existing preference optimization methods across open benchmarks on multiple evaluation metrics.