  We study a specific \textit{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 \textit{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 \textit{fixed budget} for which optimal strategies are
constructed.
