Fair Best Arm Identification with Fixed Confidence
This work addresses fairness in decision-making for applications like wireless scheduling, though it is incremental as it extends traditional BAI with constraints.
The paper tackles the problem of Best Arm Identification under fairness constraints (F-BAI), establishing a sample complexity lower bound and proposing an algorithm, F-TaS, that matches this bound while satisfying fairness constraints, with numerical results showing efficiency in minimizing sample complexity and achieving low fairness violations.
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.