In the adaptive setting, many multi-armed bandit applications allow the learner to adaptively draw samples and adjust sampling strategy in rounds. In many real applications, not only the query complexity but also the round complexity need to be optimized. In this paper, we study both PAC and exact top-k arm identification problems and design efficient algorithms considering both round complexity and query complexity.

In the adaptive setting, many multi-armed bandit applications allow the learner to adaptively draw samples and adjust sampling strategy in rounds. In many real applications, not only the query complexity but also the round complexity need to be optimized. In this paper, we study both PAC and exact top-k arm identification problems and design efficient algorithms considering both round complexity and query complexity.