Best Group Identification in Multi-Objective Bandits

TL;DR

This paper studies identifying the best groups in a multi-objective bandit setting, proposing algorithms for two formulations, with theoretical bounds and empirical validation.

Contribution

It introduces the Best Group Identification problem, develops elimination algorithms, and provides sample complexity bounds for multi-objective bandit group selection.

Findings

Algorithms achieve strong empirical performance.

Upper and lower bounds on sample complexity are established.

Effective identification of optimal groups in multi-objective settings.

Abstract

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.