NeurIPS 2018spotlight135 citations
Wasserstein Distributionally Robust Kalman Filtering
Soroosh Shafieezadeh-Abadeh, Viet Anh Nguyen, Daniel Huhn, Peyman Mohajerin Esfahani
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.
BibTeX
@inproceedings{NEURIPS2018_15212f24,
author = {Shafieezadeh Abadeh, Soroosh and Nguyen, Viet Anh and Kuhn, Daniel and Mohajerin Esfahani, Peyman Mohajerin},
booktitle = {Advances in Neural Information Processing Systems},
editor = {S. Bengio and H. Wallach and H. Larochelle and K. Grauman and N. Cesa-Bianchi and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Wasserstein Distributionally Robust Kalman Filtering},
url = {https://proceedings.neurips.cc/paper_files/paper/2018/file/15212f24321aa2c3dc8e9acf820f3c15-Paper.pdf},
volume = {31},
year = {2018}
}