Selection of the Best Policy under Fairness Constraints for Subpopulations

TL;DR

This paper introduces a formal framework and an efficient algorithm for selecting the best policy under fairness constraints across subpopulations, ensuring minimum performance standards.

Contribution

It formalizes the SBFC problem, derives a lower bound on sample complexity, and proposes an optimal algorithm with extensions to various fairness specifications.

Findings

The SBFC problem has a proven instance-specific lower bound.

The T-a-S-CS algorithm asymptotically achieves this lower bound.

Numerical experiments show substantial efficiency gains over baselines.

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.