Wasserstein Distributionally Robust Kalman Filtering

Part of Advances in Neural Information Processing Systems 31 (NeurIPS 2018)

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Soroosh Shafieezadeh Abadeh, Viet Anh Nguyen, Daniel Kuhn, Peyman Mohajerin Mohajerin Esfahani


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.