Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamics

Asaf B Cassel, Alon Cohen, Tomer Koren
Proceedings of Thirty Fifth Conference on Learning Theory, PMLR 178:3589-3604, 2022.

Abstract

We consider the problem of controlling an unknown linear dynamical system under a stochastic convex cost and full feedback of both the state and cost function. We present a computationally efficient algorithm that attains an optimal $\sqrt{T}$ regret-rate against the best stabilizing linear controller. In contrast to previous work, our algorithm is based on the Optimism in the Face of Uncertainty paradigm. This results in a substantially improved computational complexity and a simpler analysis.

Cite this Paper

BibTeX
@InProceedings{pmlr-v178-cassel22a, title = {Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamics}, author = {Cassel, Asaf B and Cohen, Alon and Koren, Tomer}, booktitle = {Proceedings of Thirty Fifth Conference on Learning Theory}, pages = {3589--3604}, year = {2022}, editor = {Loh, Po-Ling and Raginsky, Maxim}, volume = {178}, series = {Proceedings of Machine Learning Research}, month = {02--05 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v178/cassel22a/cassel22a.pdf}, url = {https://proceedings.mlr.press/v178/cassel22a.html}, abstract = {We consider the problem of controlling an unknown linear dynamical system under a stochastic convex cost and full feedback of both the state and cost function. We present a computationally efficient algorithm that attains an optimal $\sqrt{T}$ regret-rate against the best stabilizing linear controller. In contrast to previous work, our algorithm is based on the Optimism in the Face of Uncertainty paradigm. This results in a substantially improved computational complexity and a simpler analysis.} }
Endnote
%0 Conference Paper %T Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamics %A Asaf B Cassel %A Alon Cohen %A Tomer Koren %B Proceedings of Thirty Fifth Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2022 %E Po-Ling Loh %E Maxim Raginsky %F pmlr-v178-cassel22a %I PMLR %P 3589--3604 %U https://proceedings.mlr.press/v178/cassel22a.html %V 178 %X We consider the problem of controlling an unknown linear dynamical system under a stochastic convex cost and full feedback of both the state and cost function. We present a computationally efficient algorithm that attains an optimal $\sqrt{T}$ regret-rate against the best stabilizing linear controller. In contrast to previous work, our algorithm is based on the Optimism in the Face of Uncertainty paradigm. This results in a substantially improved computational complexity and a simpler analysis.
APA
Cassel, A.B., Cohen, A. & Koren, T.. (2022). Efficient Online Linear Control with Stochastic Convex Costs and Unknown Dynamics. Proceedings of Thirty Fifth Conference on Learning Theory, in Proceedings of Machine Learning Research 178:3589-3604 Available from https://proceedings.mlr.press/v178/cassel22a.html.

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