在公平约束下选出最优政策，确保各子群体表现达标。
Selection of the Best Policy under Fairness Constraints for Subpopulations
- 提出公平约束下的最优政策选择框架SBFC
- 算法渐近达到理论最低样本需求，效率显著提升
- 适用于医疗、公共政策等需公平性的决策场景
医疗、公共政策和临床研发中的高风险决策常需在异质人群中统一执行单一政策。监管与公平标准要求所选政策在每个预定义子群体中表现均达最低阈值，而不仅平均表现良好。本文将此问题形式化为带公平约束的最优政策选择（SBFC），旨在从满足子群体最低表现要求的政策中选出平均性能最高的。我们建立了该问题的实例相关样本复杂度下界，并提出一种满足约束的追踪-停止算法（T-a-S-CS），可渐近达到该下界。进一步扩展至广义闭集与基于惩罚的公平性规范，保持理论保证。数值实验及国际卒中试验案例表明，该方法相比传统策略分配在效率上大幅提升。
原文摘要 · Abstract (English)
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.
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