Regret Bounds for the Adaptive Control of Linear Quadratic Systems
Abstract
We study the average cost Linear Quadratic (LQ) control problem with unknown model parameters, also known as the adaptive control problem in the control community. We design an algorithm and prove that apart from logarithmic factors its regret up to time $T$ is $O(\sqrt{T})$. Unlike previous approaches that use a forced-exploration scheme, we construct a high-probability confidence set around the model parameters and design an algorithm that plays optimistically with respect to this confidence set. The construction of the confidence set is based on the recent results from online least-squares estimation and leads to improved worst-case regret bound for the proposed algorithm. To the best of our knowledge this is the the first time that a regret bound is derived for the LQ control problem.
Cite
Text
Abbasi-Yadkori and Szepesvári. "Regret Bounds for the Adaptive Control of Linear Quadratic Systems." Proceedings of the 24th Annual Conference on Learning Theory, 2011.Markdown
[Abbasi-Yadkori and Szepesvári. "Regret Bounds for the Adaptive Control of Linear Quadratic Systems." Proceedings of the 24th Annual Conference on Learning Theory, 2011.](https://mlanthology.org/colt/2011/abbasiyadkori2011colt-regret/)BibTeX
@inproceedings{abbasiyadkori2011colt-regret,
title = {{Regret Bounds for the Adaptive Control of Linear Quadratic Systems}},
author = {Abbasi-Yadkori, Yasin and Szepesvári, Csaba},
booktitle = {Proceedings of the 24th Annual Conference on Learning Theory},
year = {2011},
pages = {1-26},
volume = {19},
url = {https://mlanthology.org/colt/2011/abbasiyadkori2011colt-regret/}
}