mlsanityData to 7 Oct 2026

Wasserstein Distributionally Robust Kalman Filtering

arXiv 1809.08830 ↗First posted 24 Sep 2018math.OC cs.LG stat.MLcited by 17

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Abstract (arXiv)

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.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 Sep 2018.

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Citing papers per year: 2021: 2; 2022: 2; 2023: 6; 2024: 2; 2025: 1; 2026: 4.

17 papers.

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  1. 2021Distributionally Robust Learningcited by 44
  2. 2023A Finite Sample Complexity Bound for Distributionally Robust Q-learningcited by 35
  3. 2023Outlier-Robust Wasserstein DROcited by 16
  4. 2021Sequential Domain Adaptation by Synthesizing Distributionally Robust Expertscited by 14
  5. 2023Nash Equilibria, Regularization and Computation in Optimal Transport-Based Distributionally Robust Optimizationcited by 8
  6. 2023Topology-aware Robust Optimization for Out-of-distribution Generalizationcited by 7
  7. 2022Wasserstein Distributionally Robust Optimization with Wasserstein Barycenterscited by 3
  8. 2024An Inexact Halpern Iteration with Application to Distributionally Robust Optimizationcited by 2
  9. 2024A Geometric Unification of Distributionally Robust Covariance Estimators: Shrinking the Spectrum by Inflating the Ambiguity Setcited by 2
  10. 2022Towards Backwards-Compatible Data with Confounded Domain Adaptationcited by 1
  11. 2023Minimax Statistical Estimation under Wasserstein Contaminationcited by 1
  12. 2025Tempering the Bayes Filter towards Improved Model-Based Estimationcited by 1
5 more
  1. 2023Propagating Kernel Ambiguity Sets in Nonlinear Data-driven Dynamics Modelscited by 0
  2. 2026Distributionally Robust K-Means Clusteringcited by 0
  3. 2026Wasserstein Distributionally Robust Risk-Sensitive Estimation via Conditional Value-at-Riskcited by 0
  4. 2026Adversarial observations in probabilistic State-Space Models for robust Reinforcement Learningcited by 0
  5. 2026Learning Perturbation Robust Policies for LLM Agents with Stable Optimizationcited by 0