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Distributionally robust optimization has been shown to offer a principled wayto regularize learning models. In this paper, we find that Tikhonovregularization is distributionally robust in an optimal transport sense (i.e.,if an adversary chooses distributions in a suitable optimal transportneighborhood of the empirical measure), provided that suitable martingaleconstraints are also imposed. Further, we introduce a relaxation of themartingale constraints which not only provides a unified viewpoint to a classof existing robust methods but also leads to new regularization tools. Torealize these novel tools, tractable computational algorithms are proposed. Asa byproduct, the strong duality theorem proved in this paper can be potentiallyapplied to other problems of independent interest.

Tikhonov Regularization is Optimal Transport Robust under Martingale Constraints