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arXiv · 1605.07162

Pure Exploration of Multi-armed Bandit Under Matroid Constraints

Lijie Chen·Anupam Gupta·Jian Li
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Abstract

We study the pure exploration problem subject to a matroid constraint (Best-Basis) in a stochastic multi-armed bandit game. In a Best-Basis instance, we are given $n$ stochastic arms with unknown reward distributions, as well as a matroid $\mathcal{M}$ over the arms. Let the weight of an arm be the mean of its reward distribution. Our goal is to identify a basis of $\mathcal{M}$ with the maximum total weight, using as few samples as possible. The problem is a significant generalization of the best arm identification problem and the top-$k$ arm identification problem, which have attracted significant attentions in recent years. We study both the exact and PAC versions of Best-Basis, and provide algorithms with nearly-optimal sample complexities for these versions. Our results generalize and/or improve on several previous results for the top-$k$ arm identification problem and the combinatorial pure exploration problem when the combinatorial constraint is a matroid.

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Lijie Chen, Anupam Gupta, Jian Li. 2016-05-25. Pure Exploration of Multi-armed Bandit Under Matroid Constraints. https://arxiv.org/abs/1605.07162

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