Statistical Learning Theory for Direct Preference Optimization
Direct Preference Optimization (DPO) learns from pairwise preferences through a logistic objective whose score-difference parameterization follows the Bradley--Terry model. We study how failure of this modeling assumption limits DPO, distinguishing structural misspecification from limited model capacity and finite-sample estimation. Our main contribution is a characterization of structural approximation error through the triangle-curl of the preference log-odds, which vanishes exactly when preferences admit a Bradley--Terry representation. We upper bound the achievable excess logistic risk by a score-class approximation term and a triangle-curl term, and establish a lower bound proportion...
| Authors | Joel Wills, Yuanfan Li, Yiming Ying et al. |
|---|---|
| Primary category | cs.LG |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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