  We study the problem of identifying the top $m$ arms in a multi-armed bandit
game. Our proposed solution relies on a new algorithm based on successive
rejects of the seemingly bad arms, and successive accepts of the good ones.
This algorithmic contribution allows to tackle other multiple identifications
settings that were previously out of reach. In particular we show that this
idea of successive accepts and rejects applies to the multi-bandit best arm
identification problem.
