Selection of the Best Policy under Fairness Constraints for Subpopulations
For decision-makers in high-stakes domains like healthcare, this work provides a theoretically grounded method to select policies that meet fairness constraints across subpopulations, improving sample efficiency over existing baselines.
The paper formalizes the problem of selecting the best policy under fairness constraints requiring adequate performance in each subpopulation, provides a lower bound on sample complexity, and develops an algorithm (T-a-S-CS) that achieves this bound asymptotically, with experiments showing substantial efficiency gains.
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.