We study the problem of adaptive control in partially observable linear
dynamical systems. We propose a novel algorithm, adaptive control online
learning algorithm (AdaptOn), which efficiently explores the environment,
estimates the system dynamics episodically and exploits these estimates to
design effective controllers to minimize the cumulative costs. Through
interaction with the environment, AdaptOn deploys online convex optimization to
optimize the controller while simultaneously learning the system dynamics to
improve the accuracy of controller updates. We show that when the cost
functions are strongly convex, after $T$ times step of agent-environment
interaction, AdaptOn achieves regret upper bound of
$polylogłeft(T\right)$. To the best of our knowledge, AdaptOn is the
first algorithm which achieves $polylogłeft(T\right)$ regret in
adaptive control of unknown partially observable linear dynamical systems which
includes linear quadratic Gaussian (LQG) control.
Description
[2003.11227] Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems
%0 Journal Article
%1 lale2020logarithmic
%A Lale, Sahin
%A Azizzadenesheli, Kamyar
%A Hassibi, Babak
%A Anandkumar, Anima
%D 2020
%K bounds control dynamic readings systems theory
%T Logarithmic Regret Bound in Partially Observable Linear Dynamical
Systems
%U http://arxiv.org/abs/2003.11227
%X We study the problem of adaptive control in partially observable linear
dynamical systems. We propose a novel algorithm, adaptive control online
learning algorithm (AdaptOn), which efficiently explores the environment,
estimates the system dynamics episodically and exploits these estimates to
design effective controllers to minimize the cumulative costs. Through
interaction with the environment, AdaptOn deploys online convex optimization to
optimize the controller while simultaneously learning the system dynamics to
improve the accuracy of controller updates. We show that when the cost
functions are strongly convex, after $T$ times step of agent-environment
interaction, AdaptOn achieves regret upper bound of
$polylogłeft(T\right)$. To the best of our knowledge, AdaptOn is the
first algorithm which achieves $polylogłeft(T\right)$ regret in
adaptive control of unknown partially observable linear dynamical systems which
includes linear quadratic Gaussian (LQG) control.
@article{lale2020logarithmic,
abstract = {We study the problem of adaptive control in partially observable linear
dynamical systems. We propose a novel algorithm, adaptive control online
learning algorithm (AdaptOn), which efficiently explores the environment,
estimates the system dynamics episodically and exploits these estimates to
design effective controllers to minimize the cumulative costs. Through
interaction with the environment, AdaptOn deploys online convex optimization to
optimize the controller while simultaneously learning the system dynamics to
improve the accuracy of controller updates. We show that when the cost
functions are strongly convex, after $T$ times step of agent-environment
interaction, AdaptOn achieves regret upper bound of
$\text{polylog}\left(T\right)$. To the best of our knowledge, AdaptOn is the
first algorithm which achieves $\text{polylog}\left(T\right)$ regret in
adaptive control of unknown partially observable linear dynamical systems which
includes linear quadratic Gaussian (LQG) control.},
added-at = {2020-05-22T00:37:19.000+0200},
author = {Lale, Sahin and Azizzadenesheli, Kamyar and Hassibi, Babak and Anandkumar, Anima},
biburl = {https://www.bibsonomy.org/bibtex/2cd17d2c09bc30607cc3294558542c84c/kirk86},
description = {[2003.11227] Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems},
interhash = {0e79dd61b5b8621f5be155cf907111fb},
intrahash = {cd17d2c09bc30607cc3294558542c84c},
keywords = {bounds control dynamic readings systems theory},
note = {cite arxiv:2003.11227},
timestamp = {2020-05-22T00:37:19.000+0200},
title = {Logarithmic Regret Bound in Partially Observable Linear Dynamical
Systems},
url = {http://arxiv.org/abs/2003.11227},
year = 2020
}