Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability
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| Format: | Preprint |
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2026
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| _version_ | 1866909029993807872 |
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| author | Zhao, Qingyue Ji, Kaixuan Zhao, Heyang Gu, Quanquan |
| author_facet | Zhao, Qingyue Ji, Kaixuan Zhao, Heyang Gu, Quanquan |
| contents | \emph{Kullback-Leibler} (KL) regularization is ubiquitous in reinforcement learning algorithms in the form of \emph{reverse} or \emph{forward} KL. Recent studies have demonstrated $ε^{-1}$-type fast rates for decision making under reverse KL regularization, in contrast to the standard $ε^{-2}$-type sample complexity. However, for forward-KL-regularized objectives, existing statistical analyses are either not applicable or result in $\tilde{O}(ε^{-2})$ slow rates. We take the first step towards addressing this problem via a streamlined analysis of forward-KL-regularized offline CBs. We give the first $\tilde{O}(ε^{-1})$ upper bounds in tabular and general function approximation settings, both under notions of \emph{single-policy concentrability}. In particular, our convex-analytical pipeline unifies these settings by exploiting the pessimism principle in a novel way and completely bypasses the proof routines in previous works based on the mean value theorem, which might be of independent interest. Moreover, we provide rate-optimal lower bounds, manifesting the tightness of our upper bounds in terms of statistical rates. Our lower bounds also demonstrate that the forward-KL-regularized sample complexity recovers the unregularized slow rate in the low-regularization regime, similarly to the reverse-KL regularization. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_09214 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability Zhao, Qingyue Ji, Kaixuan Zhao, Heyang Gu, Quanquan Machine Learning Artificial Intelligence Information Theory Statistics Theory \emph{Kullback-Leibler} (KL) regularization is ubiquitous in reinforcement learning algorithms in the form of \emph{reverse} or \emph{forward} KL. Recent studies have demonstrated $ε^{-1}$-type fast rates for decision making under reverse KL regularization, in contrast to the standard $ε^{-2}$-type sample complexity. However, for forward-KL-regularized objectives, existing statistical analyses are either not applicable or result in $\tilde{O}(ε^{-2})$ slow rates. We take the first step towards addressing this problem via a streamlined analysis of forward-KL-regularized offline CBs. We give the first $\tilde{O}(ε^{-1})$ upper bounds in tabular and general function approximation settings, both under notions of \emph{single-policy concentrability}. In particular, our convex-analytical pipeline unifies these settings by exploiting the pessimism principle in a novel way and completely bypasses the proof routines in previous works based on the mean value theorem, which might be of independent interest. Moreover, we provide rate-optimal lower bounds, manifesting the tightness of our upper bounds in terms of statistical rates. Our lower bounds also demonstrate that the forward-KL-regularized sample complexity recovers the unregularized slow rate in the low-regularization regime, similarly to the reverse-KL regularization. |
| title | Fast Rates for Offline Contextual Bandits with Forward-KL Regularization under Single-Policy Concentrability |
| topic | Machine Learning Artificial Intelligence Information Theory Statistics Theory |
| url | https://arxiv.org/abs/2605.09214 |