Max-Min Grouped Bandits
This addresses robust optimization in applications like recommendation systems, but is incremental as it builds on existing bandit frameworks.
The paper tackles the max-min grouped bandits problem, where arms are in overlapping groups and the goal is to identify the group with the highest worst-arm mean reward, presenting algorithms with sample complexity bounds and a lower bound.
In this paper, we introduce a multi-armed bandit problem termed max-min grouped bandits, in which the arms are arranged in possibly-overlapping groups, and the goal is to find the group whose worst arm has the highest mean reward. This problem is of interest in applications such as recommendation systems and resource allocation, and is also closely related to widely-studied robust optimization problems. We present two algorithms based successive elimination and robust optimization, and derive upper bounds on the number of samples to guarantee finding a max-min optimal or near-optimal group, as well as an algorithm-independent lower bound. We discuss the degree of tightness of our bounds in various cases of interest, and the difficulties in deriving uniformly tight bounds.