Exploring the Limits of the Delta Learning Hypothesis: Single-Pair Generator Biases in Direct Preference Optimization

Giuseppe Curci, Stefano Simonazzi, Andrea Molinari, Andrea Zugarini

Direct Preference Optimization (DPO) typically relies on preference pairs generated from diverse model pools and ranked by an external LLM judge. The recently proposed delta-learning hypothesis suggests that comparable supervision can instead be obtained from a single pair of models by treating the larger model's response as preferred. We investigate the limits of this approach across model families and scales. We show, both theoretically and empirically, that fixed model pairs introduce systematic, generator-dependent biases that are predictive of the preference label independent of response quality. Consequently, DPO trained on single-pair data consistently underperforms multi-model preference data, despite the larger generator producing higher-quality responses, and we trace this gap to training dynamics consistent with reward hacking on these biases. We further show that simply increasing the number of generators, even without an external judge, is enough to partially mitigate this effect. Our results highlight generator diversity as a critical factor in preference-data construction.