  We determine the sample complexity of pure exploration bandit problems with
multiple good answers. We derive a lower bound using a new game equilibrium
argument. We show how continuity and convexity properties of single-answer
problems ensures that the Track-and-Stop algorithm has asymptotically optimal
sample complexity. However, that convexity is lost when going to the
multiple-answer setting. We present a new algorithm which extends
Track-and-Stop to the multiple-answer case and has asymptotic sample complexity
matching the lower bound.
