An optimal algorithm for the Thresholding Bandit Problem

We study a specific combinatorial pure exploration stochastic bandit problem where the learner aims at finding the set of arms whose means are above a given threshold, up to a given precision, and for a fixed time horizon. We propose a parameter-free algorithm based on an original heuristic, and prove that it is optimal for this problem by deriving matching upper and lower bounds. To the best of our knowledge, this is the first non-trivial pure exploration setting with fixed budget for which provably optimal strategies are constructed.