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Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting

Lale, Sahin and Azizzadenesheli, Kamyar and Hassibi, Babak and Anandkumar, Anima (2021) Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting. In: 2021 American Control Conference (ACC). IEEE , Piscataway, NJ, pp. 2517-2522. ISBN 978-1-6654-4197-1. https://resolver.caltech.edu/CaltechAUTHORS:20200403-141835981

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Abstract

We study the problem of adaptive control in partially observable linear quadratic Gaussian control systems, where the model dynamics are unknown a priori. We propose LQGOPT, a novel adaptive control algorithm based on the principle of optimism in the face of uncertainty, to effectively minimize the overall control cost. We employ the predictor state evolution representation of the system dynamics and deploy a recently proposed closed-loop system identification method, estimation, and confidence bound construction. LQGOPT efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model for further exploration and exploitation. We provide stability guarantees for LQGOPT, and prove the first Õ(√T) regret upper bound for adaptive control of linear quadratic Gaussian (LQG) systems with convex cost, where T is the time horizon of the problem.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.23919/ACC50511.2021.9483309DOIArticle
https://arxiv.org/abs/2003.05999arXivDiscussion Paper
ORCID:
AuthorORCID
Azizzadenesheli, Kamyar0000-0001-8507-1868
Alternate Title:Regret Bound of Adaptive Control in Linear Quadratic Gaussian (LQG) Systems
Additional Information:© 2021 AACC. S. Lale is supported in part by DARPA PAI and Beyond Limits Inc. B. Hassibi is supported in part by the National Science Foundation, by NASA’s JPL through the President and Director’s Fund. A. Anandkumar is supported in part by Bren endowed chair, DARPA PAI and LwLL grants, Microsoft, Google, and Adobe faculty fellowships.
Funders:
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Beyond LimitsUNSPECIFIED
NSFUNSPECIFIED
JPL President and Director's FundUNSPECIFIED
Bren Professor of Computing and Mathematical SciencesUNSPECIFIED
Learning with Less Labels (LwLL)UNSPECIFIED
MicrosoftUNSPECIFIED
GoogleUNSPECIFIED
AdobeUNSPECIFIED
DOI:10.23919/ACC50511.2021.9483309
Record Number:CaltechAUTHORS:20200403-141835981
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200403-141835981
Official Citation:S. Lale, K. Azizzadenesheli, B. Hassibi and A. Anandkumar, "Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting," 2021 American Control Conference (ACC), 2021, pp. 2517-2522, doi: 10.23919/ACC50511.2021.9483309
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102332
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:03 Apr 2020 21:41
Last Modified:26 Aug 2021 17:54

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