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Tikhonov Regularization is Optimal Transport Robust under Martingale Constraints
Jiajin Li · Sirui Lin · Jose Blanchet · Viet Anh Nguyen

Thu Dec 01 09:00 AM -- 11:00 AM (PST) @ Hall J #726

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.

Author Information

Jiajin Li (Stanford University)
Sirui Lin (Stanford University)
Jose Blanchet (Stanford University)
Viet Anh Nguyen (EPFL)

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