Wasserstein Distributionally Robust Kalman Filtering

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.


Published in:
NIPS Proceedings, 31
Presented at:
Neural Information Processing Systems, Montréal, Canada, December 2-8, 2018
Year:
2018
Keywords:
Note:
Available from Optimization Online
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 Record created 2018-09-24, last modified 2019-03-17


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