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arXiv · 2306.09202

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

Shintaro Nakamura·Masashi Sugiyama
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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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Shintaro Nakamura, Masashi Sugiyama. 2023-06-15. A Fast Algorithm for the Real-Valued Combinatorial Pure Exploration of Multi-Armed Bandit. https://arxiv.org/abs/2306.09202

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