IFORS Distinguished Lecture by Daniel Kuhn at INFORMS Annual Meeting

Title: 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.