Selection of the Best Policy under Fairness Constraints for Subpopulations
2026-05-11 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study a problem where a single policy must be chosen to work well for all different groups in a population, not just on average. They call this the Selection of the Best with Fairness Constraints (SBFC) problem and focus on ensuring each subgroup meets a minimum performance level. They find a theoretical limit on how much data is needed and design an algorithm (T-a-S-CS) that meets this limit efficiently. The authors also expand their approach to cover more general fairness rules and show through experiments and a stroke trial case that their method outperforms simpler strategies.
Selection of the BestFairness ConstraintsSubpopulation PerformanceSample ComplexityTrack-and-Stop AlgorithmPolicy SelectionClosed-Set FairnessPenalty-Based FairnessRegulatory StandardsInternational Stroke Trial
Authors
Tingyu Zhu, Yuhang Wu, Zeyu Zheng
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.