Statistical Aspects of Wasserstein Distributionally Robust Optimization Estimators

Abstract: Wasserstein-based distributional robust optimization problems are formulated as min-max games in which a statistician chooses a parameter to minimize an expected loss against an adversary (say nature) which wishes to maximize the loss by choosing an appropriate probability model within a certain non-parametric class. Recently, these formulations have been studied in the context in which the non-parametric class chosen by nature is defined as a Wasserstein-distance neighborhood around the empirical measure. It turns out that by appropriately choosing the loss and the geometry of the Wasserstein distance one can recover a wide range of classical statistical estimators (including Lasso, Graphical Lasso, SVM, group Lasso, among many others). This talk studies a wide range of rich statistical quantities associated with these problems; for example, the optimal (in a certain sense) choice of the adversarial perturbation, weak convergence of natural confidence regions associated with these formulations, and asymptotic normality of the DRO estimators. (This talk is based on joint work with Y. Kang, K. Murthy, and N. Si.)

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Bio: Jose Blanchet is a Professor of Management Science and Engineering at Stanford. Prior to joining Stanford, Jose was a Professor in the IEOR and Statistics Departments at Columbia University, and before that he was a faculty member in the Statistics Department at Harvard. Jose is a recipient of the 2009 Best Publication Award given by the INFORMS Applied Probability Society and of the 2010 Erlang Prize. He also received a PECASE award given by NSF in 2010. He has research interests in applied probability and Monte Carlo methods. He is the Area Editor of Stochastic Models in Mathematics of Operations Research and serves on the editorial board of Stochastic Systems, Extremes, and Insurance: Mathematics and Economics.