Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models

Part of Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track

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Waïss Azizian, Franck Iutzeler, Jérôme Malick


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.