Wasserstein Distributionally Robust Kalman Filtering
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
Text
Shafieezadeh-Abadeh et al. "Wasserstein Distributionally Robust Kalman Filtering." Neural Information Processing Systems, 2018.Markdown
[Shafieezadeh-Abadeh et al. "Wasserstein Distributionally Robust Kalman Filtering." Neural Information Processing Systems, 2018.](https://mlanthology.org/neurips/2018/shafieezadehabadeh2018neurips-wasserstein/)BibTeX
@inproceedings{shafieezadehabadeh2018neurips-wasserstein,
title = {{Wasserstein Distributionally Robust Kalman Filtering}},
author = {Shafieezadeh-Abadeh, Soroosh and Nguyen, Viet Anh and Huhn, Daniel and Esfahani, Peyman Mohajerin},
booktitle = {Neural Information Processing Systems},
year = {2018},
pages = {8474-8483},
url = {https://mlanthology.org/neurips/2018/shafieezadehabadeh2018neurips-wasserstein/}
}