Infinite-Horizon Distributionally Robust Regret-Optimal Control

Taylan Kargin, Joudi Hajar, Vikrant Malik, Babak Hassibi
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:23187-23214, 2024.

Abstract

We study the infinite-horizon distributionally robust (DR) control of linear systems with quadratic costs, where disturbances have unknown, possibly time-correlated distribution within a Wasserstein-2 ambiguity set. We aim to minimize the worst-case expected regret—the excess cost of a causal policy compared to a non-causal one with access to future disturbance. Though the optimal policy lacks a finite-order state-space realization (i.e., it is non-rational), it can be characterized by a finite-dimensional parameter. Leveraging this, we develop an efficient frequency-domain algorithm to compute this optimal control policy and present a convex optimization method to construct a near-optimal state-space controller that approximates the optimal non-rational controller in the $\mathit{H}_\infty$-norm. This approach avoids solving a computationally expensive semi-definite program (SDP) that scales with the time horizon in the finite-horizon setting.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-kargin24a, title = {Infinite-Horizon Distributionally Robust Regret-Optimal Control}, author = {Kargin, Taylan and Hajar, Joudi and Malik, Vikrant and Hassibi, Babak}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {23187--23214}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/kargin24a/kargin24a.pdf}, url = {https://proceedings.mlr.press/v235/kargin24a.html}, abstract = {We study the infinite-horizon distributionally robust (DR) control of linear systems with quadratic costs, where disturbances have unknown, possibly time-correlated distribution within a Wasserstein-2 ambiguity set. We aim to minimize the worst-case expected regret—the excess cost of a causal policy compared to a non-causal one with access to future disturbance. Though the optimal policy lacks a finite-order state-space realization (i.e., it is non-rational), it can be characterized by a finite-dimensional parameter. Leveraging this, we develop an efficient frequency-domain algorithm to compute this optimal control policy and present a convex optimization method to construct a near-optimal state-space controller that approximates the optimal non-rational controller in the $\mathit{H}_\infty$-norm. This approach avoids solving a computationally expensive semi-definite program (SDP) that scales with the time horizon in the finite-horizon setting.} }
Endnote
%0 Conference Paper %T Infinite-Horizon Distributionally Robust Regret-Optimal Control %A Taylan Kargin %A Joudi Hajar %A Vikrant Malik %A Babak Hassibi %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-kargin24a %I PMLR %P 23187--23214 %U https://proceedings.mlr.press/v235/kargin24a.html %V 235 %X We study the infinite-horizon distributionally robust (DR) control of linear systems with quadratic costs, where disturbances have unknown, possibly time-correlated distribution within a Wasserstein-2 ambiguity set. We aim to minimize the worst-case expected regret—the excess cost of a causal policy compared to a non-causal one with access to future disturbance. Though the optimal policy lacks a finite-order state-space realization (i.e., it is non-rational), it can be characterized by a finite-dimensional parameter. Leveraging this, we develop an efficient frequency-domain algorithm to compute this optimal control policy and present a convex optimization method to construct a near-optimal state-space controller that approximates the optimal non-rational controller in the $\mathit{H}_\infty$-norm. This approach avoids solving a computationally expensive semi-definite program (SDP) that scales with the time horizon in the finite-horizon setting.
APA
Kargin, T., Hajar, J., Malik, V. & Hassibi, B.. (2024). Infinite-Horizon Distributionally Robust Regret-Optimal Control. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:23187-23214 Available from https://proceedings.mlr.press/v235/kargin24a.html.

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