Wasserstein Distributionally Robust Kalman Filtering
Optimization and Control
2018-10-02 v3 Machine Learning
Machine Learning
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.
Cite
@article{arxiv.1809.08830,
title = {Wasserstein Distributionally Robust Kalman Filtering},
author = {Soroosh Shafieezadeh-Abadeh and Viet Anh Nguyen and Daniel Kuhn and Peyman Mohajerin Esfahani},
journal= {arXiv preprint arXiv:1809.08830},
year = {2018}
}