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Wasserstein Distributionally Robust Kalman Filtering
Soroosh Shafieezadeh Abadeh · Viet Anh Nguyen · Daniel Kuhn · Peyman Mohajerin Esfahani

Thu Dec 06 01:40 PM -- 01:45 PM (PST) @ Room 517 CD
in Thu Track 3 -- Session 2 »

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.

Author Information

Soroosh Shafieezadeh Abadeh (EPFL)
Viet Anh Nguyen (Ecole Polytechnique Federale de Lausanne)
Daniel Kuhn (EPFL)
Peyman Mohajerin Esfahani (TU Delft)

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