Fast Best-in-Class Regret for Contextual Bandits
arXiv:2510.15483v2 Announce Type: replace Abstract: We study the problem of stochastic contextual bandits in the agnostic setting, where the goal is to compete with the best policy in a given class without assuming realizability or imposing model restrictions on losses or rewards. In this work, we establish the first fast rate for regret relative to the best-in-class policy. Our proposed algorithm updates the policy at every round by minimizing a pessimistic objective, defined as a clipped inverse-propensity estimate of the policy value plus a variance penalty. By leveraging entropy assumptions on the policy class and a H\"olderian error-bound condition (a generalization of the margin condition), we achieve fast best-in-class regret rates, including polylogarithmic rates in the parametric
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Abstract:We study the problem of stochastic contextual bandits in the agnostic setting, where the goal is to compete with the best policy in a given class without assuming realizability or imposing model restrictions on losses or rewards. In this work, we establish the first fast rate for regret relative to the best-in-class policy. Our proposed algorithm updates the policy at every round by minimizing a pessimistic objective, defined as a clipped inverse-propensity estimate of the policy value plus a variance penalty. By leveraging entropy assumptions on the policy class and a Hölderian error-bound condition (a generalization of the margin condition), we achieve fast best-in-class regret rates, including polylogarithmic rates in the parametric case. The analysis is driven by a sequential self-normalized maximal inequality for bounded martingale empirical processes, which yields uniform variance-adaptive confidence bounds and guarantees pessimism under adaptive data collection.
Subjects:
Machine Learning (stat.ML); Machine Learning (cs.LG)
Cite as: arXiv:2510.15483 [stat.ML]
(or arXiv:2510.15483v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2510.15483
arXiv-issued DOI via DataCite
Submission history
From: Houssam Zenati [view email] [v1] Fri, 17 Oct 2025 09:53:42 UTC (464 KB) [v2] Fri, 3 Apr 2026 17:49:49 UTC (671 KB)
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