Best Group Identification in Multi-Objective Bandits
This addresses a novel problem in multi-armed bandits for scenarios requiring group-level decisions with multiple objectives, though it appears incremental as it extends existing bandit frameworks to groups.
The paper tackles the problem of identifying optimal groups in multi-objective multi-armed bandits with vector-valued rewards, proposing elimination-based algorithms that achieve strong empirical performance and establishing theoretical sample complexity bounds.
We introduce the Best Group Identification problem in a multi-objective multi-armed bandit setting, where an agent interacts with groups of arms with vector-valued rewards. The performance of a group is determined by an efficiency vector which represents the group's best attainable rewards across different dimensions. The objective is to identify the set of optimal groups in the fixed-confidence setting. We investigate two key formulations: group Pareto set identification, where efficiency vectors of optimal groups are Pareto optimal and linear best group identification, where each reward dimension has a known weight and the optimal group maximizes the weighted sum of its efficiency vector's entries. For both settings, we propose elimination-based algorithms, establish upper bounds on their sample complexity, and derive lower bounds that apply to any correct algorithm. Through numerical experiments, we demonstrate the strong empirical performance of the proposed algorithms.