Max-Min Grouped Bandits

• URL: http://arxiv.org/abs/2111.08862v1
• Date: Wed, 17 Nov 2021 01:59:15 GMT
• Title: Max-Min Grouped Bandits
• Authors: Zhenlin Wang and Jonathan Scarlett
• Abstract summary: We introduce a multi-armed bandit problem termed max-min grouped bandits. The goal is to find a group whose worst arm has the highest mean reward. This problem is of interest to applications such as recommendation systems.
• Score: 48.62520520818357
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 a group whose worst arm has the highest mean reward. This problem is of interest in applications such as recommendation systems, 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.

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