Optimal mass transportation is a powerful tool in the arsenal of many quantitative disciplines, with well-documented applications spanning a wide range of areas, including, operations research, economics and image analysis. In this talk, we focus on data-driven distributionally robust optimization, that is, a class of perfect-information games in which an optimizer selects an action and adversary chooses a model within a region around a baseline distribution, which we often take to be an empirical measure. We show how many machine learning algorithms can be retrieved as a special case of this type of formulation. We establish connections to regularized portfolio optimization strategies that are common in practice. These connections provide a rich intuition which allows interpreting various regularization parameters which are typically chosen in practice via cross-validation, but owing to this intuition, we are able to define a reasonable optimization criterion for choosing regularization parameters via pivotal statistics, thereby avoiding time-consuming cross-validation.
(This talk is based on joint work with Yang Kang, Karthyek Murthy and Fan Zhang).
Here are two papers which are the basis for the talk: https://arxiv.org/abs/1604.01446
Jose Blanchet is a faculty member at Stanford in the Department of MS&E. Prior to joining Stanford, he taught at Columbia and 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 worked as an analyst in Protego Financial Advisors, a leading investment bank in Mexico. He has research interests in applied probability and Monte Carlo methods. He serves on the editorial board of Advances in Applied Probability, Journal of Applied Probability, Mathematics of Operations Research, QUESTA, Stochastic Models, and Stochastic Systems.