  Distributionally robust optimization has emerged as an attractive way to
train robust machine learning models, capturing data uncertainty and
distribution shifts. Recent statistical analyses have proved that robust models
built from Wasserstein ambiguity sets have nice generalization guarantees,
breaking the curse of dimensionality. However, these results are obtained in
specific cases, at the cost of approximations, or under assumptions difficult
to verify in practice. In contrast, we establish, in this article, exact
generalization guarantees that cover all practical cases, including any
transport cost function and any loss function, potentially non-convex and
nonsmooth. For instance, our result applies to deep learning, without requiring
restrictive assumptions. We achieve this result through a novel proof technique
that combines nonsmooth analysis rationale with classical concentration
results. Our approach is general enough to extend to the recent versions of
Wasserstein/Sinkhorn distributionally robust problems that involve (double)
regularizations.
