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This research introduces a novel algorithm for stochastic contextual bandits that achieves fast best-in-class regret rates without relying on realizability assumptions. By minimizing a pessimistic objective with variance penalties and leveraging entropy assumptions, the method delivers polylogarithmic convergence in parametric settings. The theoretical advance is significant for agnostic learning scenarios where model restrictions are absent or too strong.
Fast Best-in-Class Regret for Contextual Bandits
arXiv:2510.15483v3 Announce Type: replace-cross 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 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2510.15483 [stat.ML]
(or arXiv:2510.15483v3 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2510.15483 Focus to learn more arXiv-issued DOI via DataCite
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