Pure Exploration with Multiple Correct Answers

Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)

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Rémy Degenne, Wouter M. Koolen


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 ensure that the existing 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.