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arXiv Machine Learning By Zaile Li, Weiwei Fan, L. Jeff Hong

UCB for Large-Scale Pure Exploration: Beyond Sub-Gaussianity

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The paper studies upper confidence bound (UCB) algorithms for large‑scale pure exploration problems where the performance distributions may be heavy‑tailed and not sub‑Gaussian. It introduces a meta‑UCB framework that selects the alternative with the largest sample size as the best upon stopping, and derives a distribution‑free lower bound on the probability of correct selection. Using this bound, the authors show that the meta‑UCB algorithm achieves sample optimality in both indifference‑zone and non‑indifference‑zone settings under a uniform variance bound, and provide numerical experiments that illustrate the behavior of UCB algorithms beyond the meta‑UCB framework.

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