An Optimal Algorithm for the Real-Valued Combinatorial Pure Exploration of Multi-Armed Bandit

• URL: http://arxiv.org/abs/2306.09202v2
• Date: Thu, 14 Dec 2023 11:01:33 GMT
• Title: An Optimal Algorithm for the Real-Valued Combinatorial Pure Exploration of Multi-Armed Bandit
• Authors: Shintaro Nakamura and Masashi Sugiyama
• Abstract summary: We study the real-valued pure exploration problem in the multi-armed bandit (R-CPE-MAB) Existing methods in the R-CPE-MAB can be seen as a special case of the so-called transductive linear bandits. We propose an algorithm named the gap-based exploration (CombGapE) algorithm, whose sample complexity matches the lower bound.
• Score: 65.268245109828
• License: http://creativecommons.org/licenses/by/4.0/
• 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. Existing methods in the R-CPE-MAB and transductive linear bandits have a gap of problem-dependent constant terms and logarithmic terms between the upper and lower bounds of the sample complexity, respectively. We close these gaps by proposing an algorithm named the combinatorial gap-based exploration (CombGapE) algorithm, whose sample complexity upper bound matches the lower bound. Finally, we numerically show that the CombGapE algorithm outperforms existing methods significantly.

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