Abstract: Many decision problems in science, engineering, and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision making is to learn a decision from finitely many training samples that will perform well on unseen test samples. This learning task is difficult even if all training and test samples are drawn from the same distribution—especially if the dimension of the uncertainty is large relative to the training sample size. Distributionally robust optimization using optimal transport seeks data-driven decisions that perform well under the most adverse distribution within a certain Wasserstein distance from a nominal distribution constructed from the training samples. In this talk we will show that Wasserstein distributionally robust optimization motivates new estimation approaches for the inverse covariance matrix and the conditional expectation. We will argue that these novel estimators possess many conceptual and computational benefits.
Bio: Viet Anh Nguyen is a postdoctoral scholar at the Department of Management Science and Engineering, Stanford University. He is interested in very large-scale decision making under uncertainty, statistical optimization and machine learning with applications in energy systems, operations management, and data/policy analytics. He holds a B.Eng and a M.Eng from the National University of Singapore, a French engineering diploma (Diplome d’Ingenieur) from Ecole Centrale Paris, and a Ph.D. from Ecole Polytechnique Federale de Lausanne.
Viet Anh Nguyen