Fast Best-in-Class Regret for Contextual Bandits

Fuente: arXiv
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Autori principali: Girard, Samuel, Bibaut, Aurelien, Gretton, Arthur, Kallus, Nathan, Zenati, Houssam
Natura: Preprint
Pubblicazione: 2025
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author Girard, Samuel
Bibaut, Aurelien
Gretton, Arthur
Kallus, Nathan
Zenati, Houssam
author_facet Girard, Samuel
Bibaut, Aurelien
Gretton, Arthur
Kallus, Nathan
Zenati, Houssam
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2510_15483
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Fast Best-in-Class Regret for Contextual Bandits
Girard, Samuel
Bibaut, Aurelien
Gretton, Arthur
Kallus, Nathan
Zenati, Houssam
Machine Learning
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.
title Fast Best-in-Class Regret for Contextual Bandits
topic Machine Learning
url https://arxiv.org/abs/2510.15483