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
$\mathcalO(T)$ for adaptive control of linear quadratic
Gaussian (LQG) systems, where $T$ is the time horizon of the problem.
Description
[2003.05999] Regret Bound of Adaptive Control in Linear Quadratic Gaussian (LQG) Systems
%0 Journal Article
%1 lale2020regret
%A Lale, Sahin
%A Azizzadenesheli, Kamyar
%A Hassibi, Babak
%A Anandkumar, Anima
%D 2020
%K bounds control systems theory
%T Regret Bound of Adaptive Control in Linear Quadratic Gaussian (LQG)
Systems
%U http://arxiv.org/abs/2003.05999
%X 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
$\mathcalO(T)$ for adaptive control of linear quadratic
Gaussian (LQG) systems, where $T$ is the time horizon of the problem.
@article{lale2020regret,
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.},
added-at = {2020-05-22T03:36:59.000+0200},
author = {Lale, Sahin and Azizzadenesheli, Kamyar and Hassibi, Babak and Anandkumar, Anima},
biburl = {https://www.bibsonomy.org/bibtex/25c0753079be58fde973f4b6c5266102c/kirk86},
description = {[2003.05999] Regret Bound of Adaptive Control in Linear Quadratic Gaussian (LQG) Systems},
interhash = {50a40122b0bec1bc589dc24d98fd56a0},
intrahash = {5c0753079be58fde973f4b6c5266102c},
keywords = {bounds control systems theory},
note = {cite arxiv:2003.05999},
timestamp = {2020-05-22T03:36:59.000+0200},
title = {Regret Bound of Adaptive Control in Linear Quadratic Gaussian (LQG)
Systems},
url = {http://arxiv.org/abs/2003.05999},
year = 2020
}