Riccati updates for online linear quadratic control

Mohammad Akbari, Bahman Gharesifard, Tamas Linder
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:476-485, 2020.

Abstract

We study an online setting of the linear quadratic Gaussian optimal control problem on a sequence of cost functions, where similar to classical online optimization, the future decisions are made by only knowing the cost in hindsight. We introduce a modified online Riccati update that under some boundedness assumptions, leads to logarithmic regret bounds, improving the best known square-root bound. In particular, for the scalar case we achieve the logarithmic regret without any boundedness assumption. As opposed to earlier work, proposed method does not rely on solving semi-definite programs at each stage.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-akbari20a, title = {Riccati updates for online linear quadratic control}, author = {Akbari, Mohammad and Gharesifard, Bahman and Linder, Tamas}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {476--485}, year = {2020}, editor = {Bayen, Alexandre M. and Jadbabaie, Ali and Pappas, George and Parrilo, Pablo A. and Recht, Benjamin and Tomlin, Claire and Zeilinger, Melanie}, volume = {120}, series = {Proceedings of Machine Learning Research}, month = {10--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v120/akbari20a/akbari20a.pdf}, url = {https://proceedings.mlr.press/v120/akbari20a.html}, abstract = {We study an online setting of the linear quadratic Gaussian optimal control problem on a sequence of cost functions, where similar to classical online optimization, the future decisions are made by only knowing the cost in hindsight. We introduce a modified online Riccati update that under some boundedness assumptions, leads to logarithmic regret bounds, improving the best known square-root bound. In particular, for the scalar case we achieve the logarithmic regret without any boundedness assumption. As opposed to earlier work, proposed method does not rely on solving semi-definite programs at each stage.} }
Endnote
%0 Conference Paper %T Riccati updates for online linear quadratic control %A Mohammad Akbari %A Bahman Gharesifard %A Tamas Linder %B Proceedings of the 2nd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2020 %E Alexandre M. Bayen %E Ali Jadbabaie %E George Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire Tomlin %E Melanie Zeilinger %F pmlr-v120-akbari20a %I PMLR %P 476--485 %U https://proceedings.mlr.press/v120/akbari20a.html %V 120 %X We study an online setting of the linear quadratic Gaussian optimal control problem on a sequence of cost functions, where similar to classical online optimization, the future decisions are made by only knowing the cost in hindsight. We introduce a modified online Riccati update that under some boundedness assumptions, leads to logarithmic regret bounds, improving the best known square-root bound. In particular, for the scalar case we achieve the logarithmic regret without any boundedness assumption. As opposed to earlier work, proposed method does not rely on solving semi-definite programs at each stage.
APA
Akbari, M., Gharesifard, B. & Linder, T.. (2020). Riccati updates for online linear quadratic control. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:476-485 Available from https://proceedings.mlr.press/v120/akbari20a.html.

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