Shafieezadeh Abadeh, SorooshNguyen, Viet AnhKuhn, DanielMohajerin Esfahani, Peyman2018-09-242018-09-242018-09-242018https://infoscience.epfl.ch/handle/20.500.14299/148569WOS:000461852003007We 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.Distributionally robust optimizationWasserstein metricMinimum Mean Square ErrorKalman Filtertext::conference output::conference proceedings::conference paper