Selection of the Best Policy under Fairness Constraints for Subpopulations

2026-05-10

AI Summary

This work addresses the challenge of selecting a single policy in heterogeneous populations while satisfying fairness constraints across predefined subgroups, rather than merely optimizing overall average performance. The problem is formalized as Fairness-Constrained Best Policy Selection (SBFC), for which the authors establish the first instance-dependent lower bound on sample complexity. They propose the Track-and-Stop with Constraints Sampling (T-a-S-CS) algorithm, which asymptotically achieves this lower bound. Built upon a multi-armed bandit framework, the method integrates a Track-and-Stop mechanism with explicit handling of subgroup fairness constraints, accommodating both general closed-set and penalty-based fairness notions. Empirical evaluations demonstrate that the proposed approach significantly improves sample efficiency and policy selection performance over existing baselines in real-world scenarios such as the International Stroke Trial.

Abstract

Many high-stakes decisions in health care, public policy, and clinical development require committing to a single policy that will be applied uniformly across a heterogeneous population. Regulatory and fairness standards sometime requires that the chosen policy performs adequately in every pre-specified subpopulation, not only on average. We formalize this as a Selection of the Best with Fairness Constraints (SBFC) problem, in order to identify the policy with the highest average performance among those policies that meet a minimum per-subpopulation threshold. We establish an instance-specific lower bound on sample complexity of the SBFC problem. We then develop a Track-and-Stop with Constraints on Subpopulation (T-a-S-CS) algorithm that achieves the lower bound asymptotically. We extend the framework to general closed-set and penalty-based fairness specifications with matching guarantees. Numerical experiments and a case study using the International Stroke Trial demonstrate substantial efficiency gains over policy-level allocation baselines.

Problem

• fairness constraints
• subpopulations
• policy selection
• sample complexity
• best-arm identification

Innovation

• fairness constraints
• best-arm identification
• sample complexity
• Track-and-Stop algorithm
• subpopulation fairness