Max K-armed bandit: On the ExtremeHunter algorithm and beyond

TL;DR

This paper advances the understanding of the max K-armed bandit problem by refining the analysis of the ExtremeHunter algorithm and proposing a reduction to classical bandit problems, supported by numerical comparisons.

Contribution

It refines the analysis of ExtremeHunter and introduces a reduction of Extreme Bandits to classical bandit problems, offering new theoretical insights.

Findings

Refined analysis of ExtremeHunter algorithm

Proposed reduction of Extreme Bandits to classical bandit problems

Numerical experiments comparing approaches

Abstract

This paper is devoted to the study of the max K-armed bandit problem, which consists in sequentially allocating resources in order to detect extreme values. Our contribution is twofold. We first significantly refine the analysis of the ExtremeHunter algorithm carried out in Carpentier and Valko (2014), and next propose an alternative approach, showing that, remarkably, Extreme Bandits can be reduced to a classical version of the bandit problem to a certain extent. Beyond the formal analysis, these two approaches are compared through numerical experiments.