Coverage Improvement and Fast Convergence of On-policy Preference Learning
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| Format: | Preprint |
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2026
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| _version_ | 1866911371806900224 |
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| author | Kim, Juno Yun, Jihun Lee, Jason D. Jun, Kwang-Sung |
| author_facet | Kim, Juno Yun, Jihun Lee, Jason D. Jun, Kwang-Sung |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08421 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coverage Improvement and Fast Convergence of On-policy Preference Learning Kim, Juno Yun, Jihun Lee, Jason D. Jun, Kwang-Sung Machine Learning 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. |
| title | Coverage Improvement and Fast Convergence of On-policy Preference Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.08421 |