Title of Presentation: Distributionally Robust Optimization: The Science of Underpromising and Overdelivering

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. Wasserstein distributionally robust optimization (DRO) 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. It has a wide range of conceptual, statistical and computational benefits. Most prominently, the optimal decisions can often be computed efficiently, and they enjoy provable out-of-sample and asymptotic consistency guarantees. This talk will highlight two recent advances in Wasserstein DRO. First, we will develop a principled approach to leveraging samples from heterogeneous data sources for making better decisions. In addition, we will prove the optimality of linear policies in Wasserstein distributionally robust linear-quadratic control problems with imperfect state observations, and we will show that these policies can be computed efficiently using dynamic programming, Kalman filtering and automatic differentiation.

Bio

Daniel Kuhn is a Professor of Operations Research in the College of Management of Technology at EPFL, where he holds the Chair of Risk Analytics and Optimization. His research interests revolve around stochastic, robust and distributionally robust optimization, and his principal goal is to develop efficient algorithms as well as statistical guarantees for data-driven optimization problems. This work is primarily application-driven, the main application areas being energy systems, machine learning, business analytics and finance. Before joining EPFL, Daniel Kuhn was a faculty member in the Department of Computing at Imperial College London and a postdoctoral researcher in the Department of Management Science and Engineering at Stanford University. He holds a PhD degree in Economics from the University of St. Gallen and an MSc degree in Theoretical Physics from ETH Zurich. He is an INFORMS fellow and the recipient of several research and teaching prizes including the Friedrich Wilhelm Bessel Research Award by the Alexander von Humboldt Foundation and the Frederick W. Lanchester Prize by INFORMS. He is the editor-in-chief of Mathematical Programming and the area editor for continuous optimization of Operations Research.