Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models
This work addresses a foundational issue in robust machine learning by offering exact guarantees that improve reliability for uncertain prediction tasks, though it is incremental in extending existing theory.
The paper tackles the problem of providing generalization guarantees for Wasserstein distributionally robust models, showing that these guarantees hold broadly without dimensionality issues and extend to distribution shifts and regularized versions.
Wasserstein distributionally robust estimators have emerged as powerful models for prediction and decision-making under uncertainty. These estimators provide attractive generalization guarantees: the robust objective obtained from the training distribution is an exact upper bound on the true risk with high probability. However, existing guarantees either suffer from the curse of dimensionality, are restricted to specific settings, or lead to spurious error terms. In this paper, we show that these generalization guarantees actually hold on general classes of models, do not suffer from the curse of dimensionality, and can even cover distribution shifts at testing. We also prove that these results carry over to the newly-introduced regularized versions of Wasserstein distributionally robust problems.