Speaker: Beatrice Acciaio
Title: Sensitivity of Distributionally Robust Optimization in the Adapted Bures–Wasserstein Space
Abstract: The adapted Wasserstein distance provides a natural framework for comparing stochastic processes while accounting for their temporal structure and the flow of information, especially for the purpose of dynamic stochastic optimization in a context of model uncertainty. When restricted to Gaussian processes, it gives rise to the adapted Bures–Wasserstein space, an analogue of the classical Bures–Wasserstein geometry in optimal transport. In this talk, I will present a complete geometric analysis of such space, and provide an explicit characterization of the solutions to the adapted transport problem. I will then explore how this geometric structure can be used to study the sensitivity of dynamic stochastic optimization problems with respect to perturbations of the underlying process distribution. The adapted Bures–Wasserstein distance allows us to quantify such perturbations in a way that respects the information structure of the problem, providing a framework for analyzing the stability and sensitivity of optimal values and decisions. Based on joint works with D. Bartl, A. Grass, S. Hou and G. Pammer.