Stable Preference Optimization: A Bilevel Approach to Catastrophic Preference Shift

Direct Preference Learning has emerged as a dominant offline paradigm for preference optimization. Most of these methods are based on the Bradley-Terry (BT) model for pairwise preference ranking, which directly aligns language model with human preference. Prior work has observed a counter-intuitive phenomenon termed likelihood displacement, where the absolute probability of preferred responses decreases simultaneously during training. We demonstrate that such displacement can lead to a more devastating failure mode, which we defined as textitCatastrophic Preference Shift, where the lost preference probability mass inadvertently shifts toward out-of-distribution (OOD) responses. Such a failure mode is a key limitation shared across BT-style direct preference learning methods, due to the fundamental conflict between the unconstrained discriminative alignment and generative foundational capabilities, ultimately leading to severe performance degradation (e.g., SimPO suffers a significant drop in reasoning accuracy from 73.5% to 37.5%). We analyze existing BT-style methods from the probability evolution perspective and theoretically prove that these methods exhibit over-reliance on model initialization and can lead to preference shift. To resolve these counter-intuitive behaviors, we propose a theoretically grounded Stable Preference Optimization (SPO) framework that constrains preference learning within a safe alignment region. Empirical evaluations demonstrate that SPO effectively stabilizes and enhances the performance of existing BT-style preference learning methods. SPO provides new insights into the design of preference learning objectives and opens up new avenues towards more reliable and interpretable language model alignment.