Tikhonov Regularization is Optimal Transport Robust under Martingale Constraints

Jiajin Li · Sirui Lin · Jose Blanchet · Viet Anh Nguyen

Hall J #726

Keywords: [ Tikhonov Regularization ] [ Distributionally Robust Optimization ] [ optimal transport ]


Distributionally robust optimization (DRO) has been shown to offer a principled way to regularize learning models. In this paper, we find that Tikhonov regularization is distributionally robust in an optimal transport sense (i.e. if an adversary chooses distributions in a suitable optimal transport neighborhood of the empirical measure), provided that suitable martingale constraints are also imposed. Further, we introduce a relaxation of the martingale constraints which not only provide a unified viewpoint to a class of existing robust methods but also lead to new regularization tools. To realize these novel tools, provably efficient computational algorithms are proposed. As a byproduct, the strong duality theorem proved in this paper can be potentially applied to other problems of independent interest.

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