Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets

Feras Al Taha, Eilyan Bitar
Proceedings of The 8th Annual Learning for Dynamics and Control Conference, PMLR 331:848-871, 2026.

Abstract

We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose mean and covariance lie within norm balls centered at given nominal values. To cope with this ambiguity, we design causal affine control policies to minimize the worst-case expected regret over all distributions in the ambiguity set. The resulting minimax optimal control problem is shown to admit an equivalent reformulation as a tractable convex program, which can be interpreted as a regularized version of the nominal linear-quadratic stochastic control problem. Based on the dual of this convex reformulation, we develop a scalable projected subgradient method for computing optimal controllers to arbitrary accuracy. Numerical experiments are provided to compare the proposed method with state-of-the-art data-driven control design methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v331-taha26a, title = {Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets}, author = {Taha, Feras Al and Bitar, Eilyan}, booktitle = {Proceedings of The 8th Annual Learning for Dynamics and Control Conference}, pages = {848--871}, year = {2026}, editor = {Sukhatme, Gaurav and Lindemann, Lars and Tu, Stephen and Wierman, Adam and Atanasov, Nikolay}, volume = {331}, series = {Proceedings of Machine Learning Research}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v331/main/assets/taha26a/taha26a.pdf}, url = {https://proceedings.mlr.press/v331/taha26a.html}, abstract = {We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose mean and covariance lie within norm balls centered at given nominal values. To cope with this ambiguity, we design causal affine control policies to minimize the worst-case expected regret over all distributions in the ambiguity set. The resulting minimax optimal control problem is shown to admit an equivalent reformulation as a tractable convex program, which can be interpreted as a regularized version of the nominal linear-quadratic stochastic control problem. Based on the dual of this convex reformulation, we develop a scalable projected subgradient method for computing optimal controllers to arbitrary accuracy. Numerical experiments are provided to compare the proposed method with state-of-the-art data-driven control design methods.} }
Endnote
%0 Conference Paper %T Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets %A Feras Al Taha %A Eilyan Bitar %B Proceedings of The 8th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2026 %E Gaurav Sukhatme %E Lars Lindemann %E Stephen Tu %E Adam Wierman %E Nikolay Atanasov %F pmlr-v331-taha26a %I PMLR %P 848--871 %U https://proceedings.mlr.press/v331/taha26a.html %V 331 %X We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose mean and covariance lie within norm balls centered at given nominal values. To cope with this ambiguity, we design causal affine control policies to minimize the worst-case expected regret over all distributions in the ambiguity set. The resulting minimax optimal control problem is shown to admit an equivalent reformulation as a tractable convex program, which can be interpreted as a regularized version of the nominal linear-quadratic stochastic control problem. Based on the dual of this convex reformulation, we develop a scalable projected subgradient method for computing optimal controllers to arbitrary accuracy. Numerical experiments are provided to compare the proposed method with state-of-the-art data-driven control design methods.
APA
Taha, F.A. & Bitar, E.. (2026). Distributionally Robust Regret Optimal Control Under Moment-Based Ambiguity Sets. Proceedings of The 8th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 331:848-871 Available from https://proceedings.mlr.press/v331/taha26a.html.

Related Material