A Fast Algorithm for the Real-Valued Combinatorial Pure Exploration of Multi-Armed Bandit

TL;DR

This paper introduces a new combinatorial gap-based exploration algorithm for the real-valued pure exploration problem in stochastic multi-armed bandits, achieving near-optimal sample complexity and outperforming existing methods.

Contribution

The paper presents the CombGapE algorithm, which efficiently solves the R-CPE-MAB problem with polynomial action set size, matching lower bounds up to constants.

Findings

CombGapE algorithm has near-optimal sample complexity.

Outperforms existing methods in synthetic and real datasets.

Applicable to polynomial-sized action sets in multi-armed bandits.

Abstract

We study the real-valued combinatorial pure exploration problem in the stochastic multi-armed bandit (R-CPE-MAB). We study the case where the size of the action set is polynomial with respect to the number of arms. In such a case, the R-CPE-MAB can be seen as a special case of the so-called transductive linear bandits. We introduce an algorithm named the combinatorial gap-based exploration (CombGapE) algorithm, whose sample complexity upper bound matches the lower bound up to a problem-dependent constant factor. We numerically show that the CombGapE algorithm outperforms existing methods significantly in both synthetic and real-world datasets.