Minimax Optimal Estimation of Stability Under Distribution Shift

• 成果类型: Article; Early Access
• 署名作者: Namkoong, Hongseok; Ma, Yuanzhe; Glynn, Peter W.
• 署名单位: Columbia University; Columbia University; Stanford University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2022.0658
• 发表日期: 2025
• 关键词: global sensitivity-analysis; tutorial input uncertainty; convex delay costs; External validity; robust analysis; medical-care; MODEL; RISK; CONVERGENCE; performance

摘要

The performance of decision policies and prediction models often deteriorates when applied to environments different from the ones seen during training. To ensure reliable operation, we analyze the stability of a system under distribution shift, which is defined as the smallest change in the underlying environment that causes the system's performance to deteriorate beyond a permissible threshold. In contrast to standard tail risk measures and distributionally robust losses that require the specification of a plausible magnitude of distribution shift, the stability measure is defined in terms of a more intuitive quantity: the level of acceptable performance degradation. We develop a minimax optimal estimator of stability and analyze its convergence rate, which exhibits a fundamental phase shift behavior. Our characterization of the minimax convergence rate shows that evaluating stability against large performance degradation incurs a statistical cost. Empirically, we demonstrate the practical utility of our stability framework by using it to compare system designs on problems where robustness to distribution shift is critical.