Pure Exploration and Regret Minimization in Matching Bandits

07/31/2021

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by   Flore Sentenac, et al.

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Finding an optimal matching in a weighted graph is a standard combinatorial problem. We consider its semi-bandit version where either a pair or a full matching is sampled sequentially. We prove that it is possible to leverage a rank-1 assumption on the adjacency matrix to reduce the sample complexity and the regret of off-the-shelf algorithms up to reaching a linear dependency in the number of vertices (up to poly log terms).