Fair Best Arm Identification with Fixed Confidence

TL;DR

This paper introduces a new framework for fair best arm identification that incorporates fairness constraints into the sampling process, providing theoretical bounds and an efficient algorithm validated by experiments.

Contribution

It formulates the F-BAI problem with fairness constraints, derives lower bounds, and proposes F-TaS, an algorithm that matches these bounds while satisfying fairness.

Findings

F-TaS matches the theoretical sample complexity lower bound.

The framework effectively balances fairness and efficiency.

Numerical results demonstrate low fairness violations and sample complexity.

Abstract

In this work, we present a novel framework for Best Arm Identification (BAI) under fairness constraints, a setting that we refer to as \textit{F-BAI} (fair BAI). Unlike traditional BAI, which solely focuses on identifying the optimal arm with minimal sample complexity, F-BAI also includes a set of fairness constraints. These constraints impose a lower limit on the selection rate of each arm and can be either model-agnostic or model-dependent. For this setting, we establish an instance-specific sample complexity lower bound and analyze the \textit{price of fairness}, quantifying how fairness impacts sample complexity. Based on the sample complexity lower bound, we propose F-TaS, an algorithm provably matching the sample complexity lower bound, while ensuring that the fairness constraints are satisfied. Numerical results, conducted using both a synthetic model and a practical wireless scheduling application, show the efficiency of F-TaS in minimizing the sample complexity while achieving low fairness violations.