Minimax Optimal Estimation of Stability Under Distribution Shift

TL;DR

This paper introduces a minimax optimal estimator for system stability under distribution shifts, providing a new way to measure and analyze how performance degrades with environmental changes.

Contribution

It develops a novel stability measure based on acceptable performance degradation and provides a minimax estimator with proven convergence rates, addressing a gap in robustness analysis.

Findings

The estimator achieves minimax optimal convergence rates.

Evaluating large performance degradation incurs higher statistical costs.

Empirical results demonstrate practical utility in robustness comparison.

Abstract

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.