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arXiv · 2510.03798

Batched Bandits with Heavy-Tailed Rewards

Yunwen Guo·Yunlun Shu·Gongyi Zhuo·Tianyu Wang
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Abstract

The batched multi-armed bandit (MAB) problem, where rewards are collected in batches, is pivotal in applications like clinical trials. While prior work assumes light-tailed reward distributions, real-world scenarios often exhibit heavy-tailed outcomes. This paper addresses this gap by introducing robust batched bandit algorithms for heavy-tailed rewards in both multi-arm and Lipschitz settings. We uncover somewhat surprising phenomena for such problems -- heavier tails require fewer batches to achieve near-optimal regret in the instance-independent setting, as well as the Lipschitz setting. In sharp contrast, in the instance-dependent setting, the number of batches required to achieve near-optimal regret does not depend on the tail heaviness.

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Yunwen Guo, Yunlun Shu, Gongyi Zhuo, Tianyu Wang. 2025-10-04. Batched Bandits with Heavy-Tailed Rewards. https://arxiv.org/abs/2510.03798

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