On Preconditioning of Decentralized Gradient-Descent When Solving a System of Linear Equations

This article considers solving an overdetermined system of linear equations in peer-to-peer multiagent networks. The network is assumed to be synchronous and strongly connected. Each agent has a set of local data points, and their goal is to compute a linear model that fits the collective data point...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on control of network systems Vol. 9; no. 2; pp. 811 - 822
Main Authors: Chakrabarti, Kushal, Gupta, Nirupam, Chopra, Nikhil
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.06.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Conditioning
Control systems
Convergence
Data points
decision/ estimation theory
Distributed algorithms/control
Eigenvalues and eigenfunctions
Linear equations
local pre-conditioning
Multiagent systems
Network systems
optimization
Peer-to-peer computing
Preconditioning
Prediction algorithms
Robustness
Robustness (mathematics)
Social networks
State estimation
ISSN:2325-5870, 2372-2533
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract This article considers solving an overdetermined system of linear equations in peer-to-peer multiagent networks. The network is assumed to be synchronous and strongly connected. Each agent has a set of local data points, and their goal is to compute a linear model that fits the collective data points. In principle, the agents can apply the decentralized gradient-descent method (DGD). However, when the data matrix is ill-conditioned , DGD requires many iterations to converge and is unstable against system noise. We propose a decentralized preconditioning technique to mitigate the deleterious effects of the data points' conditioning on the convergence rate of DGD. The proposed algorithm converges linearly , with an improved convergence rate than DGD. Considering the practical scenario where the computations performed by the agents are corrupted, we study the robustness guarantee of the proposed algorithm. In addition, we apply the proposed algorithm for solving decentralized state estimation problems. The empirical results show our proposed state predictor's favorable convergence rate and robustness against system noise compared to prominent decentralized algorithms.
AbstractList This article considers solving an overdetermined system of linear equations in peer-to-peer multiagent networks. The network is assumed to be synchronous and strongly connected. Each agent has a set of local data points, and their goal is to compute a linear model that fits the collective data points. In principle, the agents can apply the decentralized gradient-descent method (DGD). However, when the data matrix is ill-conditioned , DGD requires many iterations to converge and is unstable against system noise. We propose a decentralized preconditioning technique to mitigate the deleterious effects of the data points’ conditioning on the convergence rate of DGD. The proposed algorithm converges linearly , with an improved convergence rate than DGD. Considering the practical scenario where the computations performed by the agents are corrupted, we study the robustness guarantee of the proposed algorithm. In addition, we apply the proposed algorithm for solving decentralized state estimation problems. The empirical results show our proposed state predictor’s favorable convergence rate and robustness against system noise compared to prominent decentralized algorithms.
Author Gupta, Nirupam
Chopra, Nikhil
Chakrabarti, Kushal
Author_xml – sequence: 1
  givenname: Kushal
  orcidid: 0000-0002-6747-8709
  surname: Chakrabarti
  fullname: Chakrabarti, Kushal
  email: kchak@umd.edu
  organization: University of Maryland, College Park, MD, USA
– sequence: 2
  givenname: Nirupam
  orcidid: 0000-0003-4252-9319
  surname: Gupta
  fullname: Gupta, Nirupam
  email: nirupam.gupta@epfl.ch
  organization: École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
– sequence: 3
  givenname: Nikhil
  orcidid: 0000-0002-5365-293X
  surname: Chopra
  fullname: Chopra, Nikhil
  email: nchopra@umd.edu
  organization: University of Maryland, College Park, MD, USA
BookMark eNo9kN1LQjEYxkcYZOYfEN0Muj62D3e2XYaaBZKBRneNubPVRHd0Owb213eG0s37xfM8L_yuQSfUwQJwi9EAYyQflqPXxYAgQgYUlwwJeQG6hHJSEEZpJ8-EFUxwdAX6Ka0RQpiwdqdd8DkP8C1aU4fKN74OPnzB2sGxNTY0UW_8r63gNOrKt3sxtinf4ce3DXBRb36yXMPFMTV2m30zH6yOcLI_6JyWbsCl05tk--feA-9Pk-XouZjNpy-jx1lhiBBNUVayNIhr4zAXWlQGI0cR45aLkqzMyknpHJZi2BYpjOYEcy4qJyoyZJgZ2gP3p9xdrPcHmxq1rg8xtC8VKbmkciixaFX4pDKxTilap3bRb3U8KoxUJqkySZVJqjPJ1nN38nhr7b9e8qEUnNM_jzVw5g
CODEN ITCNAY
Cites_doi 10.1016/j.automatica.2019.108798
10.1109/TAC.2016.2612819
10.1109/TAC.2008.2009515
10.1017/CBO9781139020411
10.1016/S0024-3795(00)00219-6
10.1007/978-1-4613-0163-9
10.2307/2313703
10.1109/CDC.2016.7798514
10.1109/TAC.2019.2932031
10.1145/1464182.1464207
10.1109/TAC.2016.2560766
10.1109/CDC.2007.4434303
10.1080/00029890.2001.11919754
10.1109/TSP.2022.3223214
10.1109/TCNS.2018.2797805
10.3934/naco.2016014
10.1109/TAC.2017.2763782
10.1109/TAC.2017.2714645
10.1109/TAC.2020.3046611
10.1109/12.210171
10.23919/ChiCC.2018.8482965
10.56021/9781421407944
10.1109/TAC.2019.2894588
10.1137/16M1084316
10.1109/CDC.2017.8263792
ContentType Journal Article
Copyright Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2022
Copyright_xml – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2022
DBID 97E
RIA
RIE
AAYXX
CITATION
7SC
8FD
JQ2
L7M
L~C
L~D
DOI 10.1109/TCNS.2022.3165089
DatabaseName IEEE Xplore (IEEE)
IEEE All-Society Periodicals Package (ASPP) 1998–Present
IEEE Electronic Library (IEL)
CrossRef
Computer and Information Systems Abstracts
Technology Research Database
ProQuest Computer Science Collection
Advanced Technologies Database with Aerospace
Computer and Information Systems Abstracts – Academic
Computer and Information Systems Abstracts Professional
DatabaseTitle CrossRef
Computer and Information Systems Abstracts
Technology Research Database
Computer and Information Systems Abstracts – Academic
Advanced Technologies Database with Aerospace
ProQuest Computer Science Collection
Computer and Information Systems Abstracts Professional
DatabaseTitleList Computer and Information Systems Abstracts
Database_xml – sequence: 1
  dbid: RIE
  name: IEEE Xplore
  url: https://ieeexplore.ieee.org/
  sourceTypes: Publisher
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 2372-2533
EndPage 822
ExternalDocumentID 10_1109_TCNS_2022_3165089
9749877
Genre orig-research
GrantInformation_xml – fundername: Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung; Swiss National Science Foundation
  grantid: 200021_200477
  funderid: 10.13039/501100001711
– fundername: U.S. Department of Agriculture; USDA
  grantid: 2020-68012-31085
  funderid: 10.13039/100000199
GroupedDBID 0R~
4.4
6IK
97E
AAJGR
AARMG
AASAJ
AAWTH
ABAZT
ABJNI
ABQJQ
ABVLG
AGQYO
AGSQL
AHBIQ
AKJIK
AKQYR
ALMA_UNASSIGNED_HOLDINGS
ATWAV
BEFXN
BFFAM
BGNUA
BKEBE
BPEOZ
EBS
EJD
IFIPE
IPLJI
JAVBF
M43
OCL
PQQKQ
RIA
RIE
AAYXX
CITATION
7SC
8FD
JQ2
L7M
L~C
L~D
ID FETCH-LOGICAL-c288t-6d96c07acf178a8dc10f3057e7862bcbf99ff1984f1998ca721778df8d24515c3
IEDL.DBID RIE
ISICitedReferencesCount 1
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000815662700027&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 2325-5870
IngestDate Sun Nov 30 03:50:53 EST 2025
Sat Nov 29 06:13:49 EST 2025
Wed Aug 27 02:23:54 EDT 2025
IsDoiOpenAccess false
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2
Language English
License https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html
https://doi.org/10.15223/policy-029
https://doi.org/10.15223/policy-037
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c288t-6d96c07acf178a8dc10f3057e7862bcbf99ff1984f1998ca721778df8d24515c3
Notes ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ORCID 0000-0002-5365-293X
0000-0003-4252-9319
0000-0002-6747-8709
OpenAccessLink http://infoscience.epfl.ch/record/295277
PQID 2679394918
PQPubID 2040410
PageCount 12
ParticipantIDs crossref_primary_10_1109_TCNS_2022_3165089
proquest_journals_2679394918
ieee_primary_9749877
PublicationCentury 2000
PublicationDate 2022-06-01
PublicationDateYYYYMMDD 2022-06-01
PublicationDate_xml – month: 06
  year: 2022
  text: 2022-06-01
  day: 01
PublicationDecade 2020
PublicationPlace Piscataway
PublicationPlace_xml – name: Piscataway
PublicationTitle IEEE transactions on control of network systems
PublicationTitleAbbrev TCNS
PublicationYear 2022
Publisher IEEE
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher_xml – name: IEEE
– name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
References ref13
ref12
ref14
Nocedal (ref15) 2006
ref11
ref10
ref2
ref1
ref17
ref16
ref19
ref18
ref24
ref26
ref25
ref20
ref22
ref21
ref27
ref8
ref7
ref9
ref4
ref3
Fessler (ref23) 2020
ref6
ref5
Khalil (ref28) 2002
References_xml – ident: ref1
  doi: 10.1016/j.automatica.2019.108798
– ident: ref8
  doi: 10.1109/TAC.2016.2612819
– ident: ref2
  doi: 10.1109/TAC.2008.2009515
– ident: ref27
  doi: 10.1017/CBO9781139020411
– ident: ref22
  doi: 10.1016/S0024-3795(00)00219-6
– ident: ref17
  doi: 10.1007/978-1-4613-0163-9
– ident: ref20
  doi: 10.2307/2313703
– ident: ref4
  doi: 10.1109/CDC.2016.7798514
– ident: ref10
  doi: 10.1109/TAC.2019.2932031
– ident: ref19
  doi: 10.1145/1464182.1464207
– ident: ref24
  doi: 10.1109/TAC.2016.2560766
– ident: ref14
  doi: 10.1109/CDC.2007.4434303
– ident: ref21
  doi: 10.1080/00029890.2001.11919754
– ident: ref13
  doi: 10.1109/TSP.2022.3223214
– year: 2020
  ident: ref23
  article-title: Image reconstruction: Algorithms and analysis
– ident: ref7
  doi: 10.1109/TCNS.2018.2797805
– ident: ref9
  doi: 10.3934/naco.2016014
– ident: ref11
  doi: 10.1109/TAC.2017.2763782
– ident: ref3
  doi: 10.1109/TAC.2017.2714645
– volume-title: Nonlinear Systems
  year: 2002
  ident: ref28
– ident: ref26
  doi: 10.1109/TAC.2020.3046611
– ident: ref18
  doi: 10.1109/12.210171
– ident: ref6
  doi: 10.23919/ChiCC.2018.8482965
– ident: ref16
  doi: 10.56021/9781421407944
– ident: ref5
  doi: 10.1109/TAC.2019.2894588
– ident: ref12
  doi: 10.1137/16M1084316
– ident: ref25
  doi: 10.1109/CDC.2017.8263792
– volume-title: Numerical Optimization
  year: 2006
  ident: ref15
SSID ssj0001255873
Score 2.2299557
Snippet This article considers solving an overdetermined system of linear equations in peer-to-peer multiagent networks. The network is assumed to be synchronous and...
SourceID proquest
crossref
ieee
SourceType Aggregation Database
Index Database
Publisher
StartPage 811
SubjectTerms Algorithms
Conditioning
Control systems
Convergence
Data points
decision/ estimation theory
Distributed algorithms/control
Eigenvalues and eigenfunctions
Linear equations
local pre-conditioning
Multiagent systems
Network systems
optimization
Peer-to-peer computing
Preconditioning
Prediction algorithms
Robustness
Robustness (mathematics)
Social networks
State estimation
Title On Preconditioning of Decentralized Gradient-Descent When Solving a System of Linear Equations
URI https://ieeexplore.ieee.org/document/9749877
https://www.proquest.com/docview/2679394918
Volume 9
WOSCitedRecordID wos000815662700027&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
journalDatabaseRights – providerCode: PRVIEE
  databaseName: IEEE Xplore
  customDbUrl:
  eissn: 2372-2533
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0001255873
  issn: 2325-5870
  databaseCode: RIE
  dateStart: 20140101
  isFulltext: true
  titleUrlDefault: https://ieeexplore.ieee.org/
  providerName: IEEE
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED61FQMMvAqiUJAHJkRo4iaxPaI-YEClUgvqROT4IVVCCbQpA78e2wlVESxsHmzLuvOd7zvfA-CS2uxO69cwxjr3QkG4l5qb5GEcpIwb-BO59m3PD2Q0orMZG9fgep0Lo5RywWfqxg7dX77Mxcq6yjrG9jUQmdShTggpc7U2_ClRREm3-rgMfNaZ9kYTAwAxNrjU2iHsx9Pjeqn8UsDuVRnu_e88-7BbWY_otmT3AdRUdgg7GzUFm_DymKGxg7lyXjlbUa5RX1VhmPNPJdHdwkV6FV6_rOaEjE7O0CR_te4FxFFZx9yuM1jVyAIavJclwZdH8DQcTHv3XtVEwROY0sKLJYuFT7jQAaGcShH42sg4UcRgmVSkmjGtA0ZDbbPtBDeIkBAqNZU4NLaO6B5DI8szdQJIBiHXZleJmQ4JxyzVKRVxGkUqJjrVLbj6pm_yVtbKSBzG8FlimZFYZiQVM1rQtARdT6xo2YL2N0eSSpqWCY6NFmEhC-jp36vOYNvuXYZwtaFRLFbqHLbERzFfLi7cRfkCiMW9ew
linkProvider IEEE
linkToHtml http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV07T8MwED5BQQIGXgVRKOCBCRGauElsj6i0gCgBqQUxETl-SJVQCm3KwK_HdgICwcKWwY_ozne-73wPgCNqszutX8MY69wLBeFeZk6Sh3GQMW7gT-Tatz30SZLQx0d2NwcnX7kwSikXfKZO7ad7y5djMbOuspaxfQ1EJvOwEIUhDspsrW8elSiipF09XQY-aw07ycBAQIwNMrWWCPtx-bhuKr9UsLtXemv_-6N1WK3sR3RWMnwD5lS-CSvfqgrW4ek2R3cO6MpR5W5FY43OVRWIOXpXEl1MXKxX4Z2X9ZyQ0co5GoyfrYMBcVRWMrfzDFo10oC6r2VR8OkW3Pe6w86lV7VR8ASmtPBiyWLhEy50QCinUgS-NlJOFDFoJhOZZkzrgNFQ23w7wQ0mJIRKTSUOjbUj2ttQy8e52gEkg5Brs6rETIeEY5bpjIo4iyIVE53pBhx_0jd9KatlpA5l-Cy1zEgtM9KKGQ2oW4J-Daxo2YDmJ0fSSp6mKY6NHmEhC-ju37MOYelyeNNP-1fJ9R4s233KgK4m1IrJTO3DongrRtPJgTs0H4wIwMI
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+Preconditioning+of+Decentralized+Gradient-Descent+When+Solving+a+System+of+Linear+Equations&rft.jtitle=IEEE+transactions+on+control+of+network+systems&rft.au=Chakrabarti%2C+Kushal&rft.au=Gupta%2C+Nirupam&rft.au=Chopra%2C+Nikhil&rft.date=2022-06-01&rft.pub=The+Institute+of+Electrical+and+Electronics+Engineers%2C+Inc.+%28IEEE%29&rft.eissn=2372-2533&rft.volume=9&rft.issue=2&rft.spage=811&rft_id=info:doi/10.1109%2FTCNS.2022.3165089&rft.externalDBID=NO_FULL_TEXT
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2325-5870&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2325-5870&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2325-5870&client=summon