Center for Applied Mathematics Colloquium
Abstract: Optimal Transport (OT) seeks the most efficient way to morph one probability distribution into another one, and minimax estimation studies worst-case risk minimization problems under distributional ambiguity. It is well known that OT gives rise to a rich class of data-driven minimax models, where the decision-maker plays a zero-sum game against nature who can adversely reshape the empirical distribution of the uncertain problem parameters within a prescribed transportation budget. Even though generic OT problems are computationally hard, the Nash strategies of the decision-maker and nature in OT-based minimax problems can often be computed efficiently. In this talk we will uncover deep connections between robustification and regularization, and we will disclose striking properties of nature’s Nash strategy, which implicitly constructs an adversarial training dataset.
Bio: I am an assistant professor in the School of Operations Research and Information Engineering at Cornell University. Before that, I held positions as a postdoctoral researcher at both the Tepper School of Business at Carnegie Mellon University and the Automatic Control Laboratory at ETH Zurich. I hold a B.Sc. and M.Sc. degree in Electrical Engineering from the University of Tehran and a Ph.D. degree in Management of Technology from École Polytechnique Fédérale de Lausanne.
My primary research interests revolve around optimization under uncertainty, low-complexity decision-making and optimal transport. Most of my works fall into one of the following categories:
Designing new models and algorithms based on (distributionally) robust optimization
Statistical and computational complexity analyses of data-driven optimization problems
Structured nonconvex optimization with application in machine learning and finance