Minimax Optimal Estimation of Stability Under Distribution Shift

• URL: http://arxiv.org/abs/2212.06338v2
• Date: Tue, 25 Jun 2024 02:21:54 GMT
• Title: Minimax Optimal Estimation of Stability Under Distribution Shift
• Authors: Hongseok Namkoong, Yuanzhe Ma, Peter W. Glynn,
• Abstract summary: We analyze the stability of a system under distribution shift. The stability measure is defined in terms of a more intuitive quantity: the level of acceptable performance degradation. Our characterization of the minimax convergence rate shows that evaluating stability against large performance degradation incurs a statistical cost.
• Score: 8.893526921869137
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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