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 effectively against model risk.
Bio: Soroosh Shafieezadeh-Abadeh received a B.Sc. and an M.Sc degree in Electrical Engineering from University of Tehran, Tehran, Iran. In September 2014, he joined the Risk Analytics and Optimization chair at EPFL. His research interests revolve around optimization, machine learning, statistics, and high-dimensional data analysis.
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