(she/her/hers)
Stanford University
Mathematical Optimization, Algorithm Design and Analysis, Machine Learning
Jiajin Li is a postdoctoral researcher in the Department of Management Science and Engineering (MS&E) at Stanford University advised by Prof. Jose Blanchet. Previously, she obtained her Ph.D. in August 2021 from in Department of Systems Engineering and Engineering Management at the Chinese University of Hong Kong supervised by Prof. Anthony Man-Cho So. She obtained her bachelor's degree in Statistics from Chongqing University. Her research focuses on continuous optimization and its interplay with machine learning, operation research, and data science. She works on the algorithmic and theoretical foundation of data-driven decision-making and robust machine learning.
Tikhonov Regularization is Optimal Transport Robust under Martingale Constraints
Distributionally robust optimization 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 provides a unified viewpoint to a class of existing robust methods but also leads to new regularization tools. To realize these novel tools, tractable 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.