Coverage Improvement and Fast Convergence of On-policy Preference Learning

• URL: http://arxiv.org/abs/2601.08421v1
• Date: Tue, 13 Jan 2026 10:46:06 GMT
• Title: Coverage Improvement and Fast Convergence of On-policy Preference Learning
• Authors: Juno Kim, Jihun Yun, Jason D. Lee, Kwang-Sung Jun,
• Abstract summary: Online on-policy preference learning algorithms for language model alignment can significantly outperform their offline counterparts.<n>We analyze how the sampling policy's coverage evolves throughout on-policy training.<n>We develop principled on-policy schemes for reward distillation in the general function class setting.
• Score: 67.36750525893514
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Online on-policy preference learning algorithms for language model alignment such as online direct policy optimization (DPO) can significantly outperform their offline counterparts. We provide a theoretical explanation for this phenomenon by analyzing how the sampling policy's coverage evolves throughout on-policy training. We propose and rigorously justify the \emph{coverage improvement principle}: with sufficient batch size, each update moves into a region around the target where coverage is uniformly better, making subsequent data increasingly informative and enabling rapid convergence. In the contextual bandit setting with Bradley-Terry preferences and linear softmax policy class, we show that on-policy DPO converges exponentially in the number of iterations for batch size exceeding a generalized coverage threshold. In contrast, any learner restricted to offline samples from the initial policy suffers a slower minimax rate, leading to a sharp separation in total sample complexity. Motivated by this analysis, we further propose a simple hybrid sampler based on a novel \emph{preferential} G-optimal design, which removes dependence on coverage and guarantees convergence in just two rounds. Finally, we develop principled on-policy schemes for reward distillation in the general function class setting, and show faster noiseless rates under an alternative deviation-based notion of coverage. Experimentally, we confirm that on-policy DPO and our proposed reward distillation algorithms outperform their off-policy counterparts and enjoy stable, monotonic performance gains across iterations.

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