Statistical Properties of Robust Learning under Distributional Shifts

2026-08-13

AI Summary

This work addresses the lack of finite-sample theoretical guarantees and systematic comparisons for existing robust learning methods under distribution shift between training and deployment environments. Focusing on Distributionally Robust Optimization (DRO) and Robust Satisficing (RS), the paper establishes, for the first time, dimension-free finite-sample generalization error bounds for the target domain and introduces an information-guided hyperparameter calibration strategy that leverages partial knowledge of the distributional shift. Theoretical analysis reveals a complementary relationship between DRO and RS under partial shift information, while empirical studies in inventory network planning demonstrate their distinct response mechanisms to positively shifted demand, thereby providing principled guidance for method selection in practice.

Abstract

Distributional shifts arise when the target deployment environment differs from the source environment that generated the training data. Robust learning frameworks such as Distributionally Robust Optimization (DRO) and Robust Satisficing (RS) aim to address this challenge, yet their finite-sample guarantees under such shifts, and their systematic comparison, remain underexplored: existing analyses typically establish guarantees either in the source environment or for adversarial worst-case performance over an ambiguity set. This paper instead studies generalization error in the target environment---the excess loss under the shifted target distribution. Our contributions are threefold. First, we derive finite-sample generalization error bounds in the shifted target environment for both DRO and RS. These bounds explicitly characterize the trade-off between reduced sensitivity to shift and the regularization penalty induced by each method's robustness hyperparameter, and they avoid the curse of dimensionality associated with Wasserstein empirical concentration. Second, when partial shift information such as shift magnitude or direction is available, we propose information-directed hyperparameter calibrations and compare the two methods given the same information. Under these calibrations, and in the partial-information regimes we study, DRO and RS exhibit complementary theoretical and empirical behavior. Finally, we apply the framework to a network lot-sizing problem, using it to interpret how robust policies respond to positive shifts in the demand distribution. Together, these results fill a gap in understanding the statistical properties of robust learning methods under distributional shifts and provide a principled basis for comparing DRO and RS.

Problem

• distributional shifts
• robust learning
• generalization error
• finite-sample guarantees
• target environment

Innovation

• distributional shift
• finite-sample generalization
• Distributionally Robust Optimization
• Robust Satisficing
• hyperparameter calibration