Understanding the Impact of Sampling Quality in Direct Preference Optimization

Abstract: We study the role of the sampling distribution in Direct Preference Optimization (DPO) and aim to understand its impact on DPO's training dynamics. Our analyses show that both the solution space and the convergence behavior of DPO depend on the support and quality of the generating distribution. We first analyze how distribution of responses influences policy updates during gradient descent, drawing connections to common phenomena found in practice. We then design a simplified yet well-structured alignment model as a proxy, and develop quantitative results showing how more frequent high-quality responses amplify the gradient signal and improve the optimization landscape, leading to more effective policy learning. Our theoretical findings are supported by empirical experiments and provide a principled justification for the online DPO framework in practice.