Wasserstein Distributionally Robust Kalman Filtering¶
Authors: Soroosh Shafieezadeh-Abadeh, Viet Anh Nguyen, Daniel Kuhn, Peyman Mohajerin Esfahani
Published: 2018 ()
arXiv: 1809.08830
Summary¶
Abstract¶
We study a distributionally robust mean square error estimation problem over a nonconvex Wasserstein ambiguity set containing only normal distributions. We show that the optimal estimator and the least favorable distribution form a Nash equilibrium. Despite the non-convex nature of the ambiguity set, we prove that the estimation problem is equivalent to a tractable convex program. We further devise a Frank-Wolfe algorithm for this convex program whose direction-searching subproblem can be solved in a quasi-closed form. Using these ingredients, we introduce a distributionally robust Kalman filter that hedges against model risk.