Controlling unknown linear dynamics with bounded multiplicative regret

Jacob Carruth; Maximilian F. Eggl; Charles Fefferman; Clarence W. Rowley; Melanie Weber

doi:10.4171/RMI/1377

Controlling unknown linear dynamics with bounded multiplicative regret

Jacob Carruth, Maximilian F. Eggl, Charles Fefferman, Clarence W. Rowley, Melanie Weber

Mathematics

Princeton University

Research output: Contribution to journal › Article › peer-review

Abstract

We consider a simple control problem in which the underlying dynamics depend on a parameter that is unknown and must be learned. We exhibit a control strategy which is optimal to within a multiplicative constant. While most authors find strategies which are successful as the time horizon tends to infinity, our strategy achieves lowest expected cost up to a constant factor for a fixed time horizon.

Original language	American English
Pages (from-to)	2185-2216
Number of pages	32
Journal	Revista Matematica Iberoamericana
Volume	38
Issue number	7
DOIs	https://doi.org/10.4171/RMI/1377
State	Published - 2022

ASJC Scopus subject areas

General Mathematics

Keywords

Bounded regret
LQR control
adaptive control
competitive ratio

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10.4171/RMI/1377

Cite this

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AU - Weber, Melanie

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AB - We consider a simple control problem in which the underlying dynamics depend on a parameter that is unknown and must be learned. We exhibit a control strategy which is optimal to within a multiplicative constant. While most authors find strategies which are successful as the time horizon tends to infinity, our strategy achieves lowest expected cost up to a constant factor for a fixed time horizon.

KW - Bounded regret

KW - LQR control

KW - adaptive control

KW - competitive ratio

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Controlling unknown linear dynamics with bounded multiplicative regret

Abstract

ASJC Scopus subject areas

Keywords

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