A Fast Algorithm for the Real-Valued Combinatorial Pure Exploration of Multi-Armed Bandit
Shintaro Nakamura, Masashi Sugiyama

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.
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Auction Theory and Applications · Optimization and Search Problems
MethodsCollaborative Preference Embedding · Focus
