Tuesday, April 26th @ 11:00-12:30 PM
Jose Blanchet, Stanford
Abstract: The focus of this talk is on decision-making rules that are designed to be min-max optimal. The decision-maker chooses a policy class (e.g. affine or even non-parametric classes) and chooses a member of the policy class by playing a (min-max) game against an adversary that chooses a probability distribution in a neighborhood of a baseline model. Both players want to optimize in opposite directions a risk loss. The adversary is able to choose from a non-parametric family (typically within a Wasserstein ball around the baseline model). When this formulation is applied to standard losses (e.g. Markowitz), we recover exact regularization representations which, combined with the existence of a Nash equilibrium provide a rich interpretation in terms of the adversarial robustness of traditional techniques. In addition, these formulations provide additional insights into an optimal selection of regularization parameters which avoids the use of cross-validation. This talk is based on several papers.