DisagreementBased Combinatorial Pure Exploration: Sample Complexity Bounds and an Efficient Algorithm
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Proceedings of the ThirtySecond Conference on Learning Theory, PMLR 99:558588, 2019.
Abstract
We design new algorithms for the combinatorial pure exploration problem in the multiarm bandit framework. In this problem, we are given $K$ distributions and a collection of subsets $\mathcal{V} \subset 2^{[K]}$ of these distributions, and we would like to find the subset $v \in \mathcal{V}$ that has largest mean, while collecting, in a sequential fashion, as few samples from the distributions as possible. In both the fixed budget and fixed confidence settings, our algorithms achieve new samplecomplexity bounds that provide polynomial improvements on previous results in some settings. Via an informationtheoretic lower bound, we show that no approach based on uniform sampling can improve on ours in any regime, yielding the first interactive algorithms for this problem with this basic property. Computationally, we show how to efficiently implement our fixed confidence algorithm whenever $\mathcal{V}$ supports efficient linear optimization. Our results involve precise concentrationofmeasure arguments and a new algorithm for linear programming with exponentially many constraints.
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