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    Regret Bound of Adaptive Control in Linear Quadratic Gaussian (LQG) Systems

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    Type
    Preprint
    Authors
    Lale, Sahin
    Azizzadenesheli, Kamyar
    Hassibi, Babak
    Anandkumar, Anima
    Date
    2020-03-12
    Permanent link to this record
    http://hdl.handle.net/10754/662315
    
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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 reinforcement learning 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 propose a new approach for closed-loop system identification, 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 regret upper bound of $\tilde{\mathcal{O}}(\sqrt{T})$ for adaptive control of linear quadratic Gaussian (LQG) systems, where $T$ is the time horizon of the problem.
    Sponsors
    S. Lale is supported in part by DARPA PAI. K. Azizzadenesheli is supported in part by Raytheon and Amazon Web Service. B. Hassibi is supported in part by the National Science Foundation under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASA’s Jet Propulsion Laboratory through the President and Director’s Fund, and by King Abdullah University of Science and Technology. A. Anandkumar is supported in part by Bren endowed chair, DARPA PAIHR00111890035 and LwLL grants, Raytheon, Microsoft, Google, and Adobe faculty fellowships.
    Publisher
    arXiv
    arXiv
    2003.05999
    Additional Links
    https://arxiv.org/pdf/2003.05999
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