Controlling unknown linear dynamics with almost optimal regret

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

doi:10.4171/RMI/1511

Controlling unknown linear dynamics with almost optimal regret

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

Mathematics

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

1 Scopus citations

Abstract

Here and in a companion paper, we consider a simple control problem in which the underlying dynamics depend on a parameter a that is unknown and must be learned. In this paper, we assume that a can be any real number and we do not assume that we have a prior belief about a. We seek a control strategy that minimizes a quantity called the regret. Given any " > 0, we produce a strategy that minimizes the regret to within a multiplicative factor of .1 C "/.

Original language	English (US)
Pages (from-to)	745-806
Number of pages	62
Journal	Revista Matematica Iberoamericana
Volume	41
Issue number	2
DOIs	https://doi.org/10.4171/RMI/1511
State	Published - 2025

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

adaptive control
agnostic control
optimal control

Access to Document

10.4171/RMI/1511

Cite this

@article{d4d102ea5931439b9970c0993f797908,

title = "Controlling unknown linear dynamics with almost optimal regret",

abstract = "Here and in a companion paper, we consider a simple control problem in which the underlying dynamics depend on a parameter a that is unknown and must be learned. In this paper, we assume that a can be any real number and we do not assume that we have a prior belief about a. We seek a control strategy that minimizes a quantity called the regret. Given any {"} > 0, we produce a strategy that minimizes the regret to within a multiplicative factor of .1 C {"}/.",

keywords = "adaptive control, agnostic control, optimal control",

author = "Jacob Carruth and Eggl, {Maximilian F.} and Charles Fefferman and Rowley, {Clarence W.}",

note = "Publisher Copyright: {\textcopyright} 2024 Real Sociedad Matem{\'a}tica Espa{\~n}ola.",

year = "2025",

doi = "10.4171/RMI/1511",

language = "English (US)",

volume = "41",

pages = "745--806",

journal = "Revista Matematica Iberoamericana",

issn = "0213-2230",

publisher = "Universidad Autonoma de Madrid",

number = "2",

}

TY - JOUR

T1 - Controlling unknown linear dynamics with almost optimal regret

AU - Carruth, Jacob

AU - Eggl, Maximilian F.

AU - Fefferman, Charles

AU - Rowley, Clarence W.

PY - 2025

Y1 - 2025

N2 - Here and in a companion paper, we consider a simple control problem in which the underlying dynamics depend on a parameter a that is unknown and must be learned. In this paper, we assume that a can be any real number and we do not assume that we have a prior belief about a. We seek a control strategy that minimizes a quantity called the regret. Given any " > 0, we produce a strategy that minimizes the regret to within a multiplicative factor of .1 C "/.

AB - Here and in a companion paper, we consider a simple control problem in which the underlying dynamics depend on a parameter a that is unknown and must be learned. In this paper, we assume that a can be any real number and we do not assume that we have a prior belief about a. We seek a control strategy that minimizes a quantity called the regret. Given any " > 0, we produce a strategy that minimizes the regret to within a multiplicative factor of .1 C "/.

KW - adaptive control

KW - agnostic control

KW - optimal control

UR - http://www.scopus.com/inward/record.url?scp=105001586510&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=105001586510&partnerID=8YFLogxK

U2 - 10.4171/RMI/1511

DO - 10.4171/RMI/1511

M3 - Article

AN - SCOPUS:105001586510

SN - 0213-2230

VL - 41

SP - 745

EP - 806

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

IS - 2

ER -

Controlling unknown linear dynamics with almost optimal regret

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this