Tikhonov Regularization is Optimal Transport Robust under Martingale Constraints
Jiajin Li, Sirui Lin, Jose Blanchet, Viet Anh Nguyen
Abstract
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.
BibTeX
@inproceedings{
li2022tikhonov,
title={Tikhonov Regularization is Optimal Transport Robust under Martingale Constraints},
author={Jiajin Li and Sirui Lin and Jose Blanchet and Viet Anh Nguyen},
booktitle={Advances in Neural Information Processing Systems},
editor={Alice H. Oh and Alekh Agarwal and Danielle Belgrave and Kyunghyun Cho},
year={2022},
url={https://openreview.net/forum?id=EQgPNPwREa}
}