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.

Conference on Neural Information Processing Systems
Machine Learning

Degenne, R., & Koolen-Wijkstra, W. (2019). Pure exploration with multiple correct answers. In Advances in Neural Information Processing Systems.