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Wasserstein Distributionally Robust Kalman Filtering

Soroosh Shafieezadeh Abadeh (soroosh.shafiee***at***epfl.ch)
Viet Anh Nguyen (viet-anh.nguyen***at***epfl.ch)
Daniel Kuhn (daniel.kuhn***at***epfl.ch)
Peyman Mohajerin Esfahani (P.MohajerinEsfahani***at***tudelft.nl)

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.

Keywords: Distributionally robust optimization, Wasserstein metric, Mean Square Error Estimator, Kalman Filter

Category 1: Stochastic Programming

Category 2: Robust Optimization

Category 3: Applications -- Science and Engineering (Statistics )

Citation: Risk Analytics and Optimization Chair, EPFL

Download: [PDF]

Entry Submitted: 09/24/2018
Entry Accepted: 09/24/2018
Entry Last Modified: 10/19/2018

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