Gradients of the entropically smoothed and sampled WDRO objective converge to Clarke subgradients of the unregularized objective as regularization vanishes, yielding O(log N/√N) SGD convergence rates up to sampling error.
Attouch, Convergence de fonctionnelles convexes
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Unregularized limit of stochastic gradient method for Wasserstein distributionally robust optimization
Gradients of the entropically smoothed and sampled WDRO objective converge to Clarke subgradients of the unregularized objective as regularization vanishes, yielding O(log N/√N) SGD convergence rates up to sampling error.