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SIAM Journal on Control and OptimizationVolume 61, Issue 3, 2023, Pages 1582-1609

DISTRIBUTED RECURSIVE ESTIMATION UNDER HEAVY-TAIL COMMUNICATION NOISE(Article)

  • Jakovetic, D.,
  • Vukovic, M.,
  • Bajovic, D.,
  • Sahu, A.K.,
  • Kar, S.
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  • aFaculty of Sciences, Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia
  • bFaculty of Technical Sciences, Department of Fundamental Sciences, University of Novi Sad, Novi Sad, Serbia
  • cFaculty of Technical Sciences, Department of Power, Electronic and Communication Engineering, University of Novi Sad, Serbia
  • dAmazon Alexa AI, Seattle, WA 98109, United States
  • eDepartment of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890, United States

Abstract

We consider distributed recursive estimation of an unknown vector parameter θ* ∈ ℝM in the presence of impulsive communication noise. That is, we assume that interagent communication is subject to an additive communication noise that may have heavy-tails or is contaminated with outliers. To combat this effect, within the class of consensus+innovations distributed estimators, we introduce for the first time a nonlinearity in the consensus update. We allow for a general class of nonlinearities that subsumes, e.g., the sign function or componentwise saturation function. For the general nonlinear estimator and a general class of additive communication noises-that may have infinite moments of order higher than one-we establish almost sure convergence to the parameter θ*. We further prove asymptotic normality and evaluate the corresponding asymptotic covariance. These results reveal interesting tradeoffs between the negative effect of "loss of information"" due to incorporation of the nonlinearity and the positive effect of communication noise reduction. We also demonstrate and quantify benefits of introducing the nonlinearity in high-noise (low signal-to-noise ratio) and heavy-tail communication noise regimes. © 2023 Society for Industrial and Applied Mathematics.

Author keywords

consensus+innovationsdistributed estimationdistributed inferenceheavy-tail noiserecursive estimationstochastic approximation

Indexed keywords

Engineering controlled terms:AdditivesParameter estimationStochastic systems
Engineering uncontrolled termsCommunication noiseConsensus + innovationsDistributed estimationDistributed inferenceGeneral classHeavy-tail noiseHeavy-tailsRecursive estimationStochastic approximationsVector parameter
Engineering main heading:Signal to noise ratio

Funding details

Funding sponsor Funding number Acronym
Ministarstvo Prosvete, Nauke i Tehnološkog RazvojaMPNTR
Horizon 2020 Framework Programme
See opportunities by H2020		957337H2020
Horizon 2020871518

  • 1

    *Received by the editors February 10, 2022; accepted for publication (in revised form) January 9, 2023; published electronically June 20, 2023. https://doi.org/10.1137/22M1477015 Funding: The work of the first and third authors is supported by the European Union's Horizon 2020 Research and Innovation program under grant 957337. The work of the second author is supported by the European Union's Horizon 2020 Research and Innovation program under grant 871518. The work of the first three authors was also supported by the Serbian Ministry of Education, Science and Technological Development. \\dagger Faculty of Sciences, Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia ([email protected]). \\ddagger Faculty of Technical Sciences, Department of Fundamental Sciences, University of Novi Sad, Novi Sad, Serbia ([email protected]). \\S Faculty of Technical Sciences, Department of Power, Electronic and Communication Engineering, University of Novi Sad ([email protected]). \\P Amazon Alexa AI, Seattle, WA 98109 USA ([email protected]). \\| Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890 USA ([email protected]).

  • 2

    The work of the first and third authors is supported by the European Union's Horizon 2020 Research and Innovation program under grant 957337. The work of the second author is supported by the European Union's Horizon 2020 Research and Innovation program under grant 871518. The work of the first three authors was also supported by the Serbian Ministry of Education, Science and Technological Development.

  • ISSN: 03630129
  • CODEN: SJCOD
  • Source Type: Journal
  • Original language: English
  • DOI: 10.1137/22M1477015
  • Document Type: Article
  • Publisher: Society for Industrial and Applied Mathematics Publications


© Copyright 2023 Elsevier B.V., All rights reserved.

Cited by 2 documents

Bajovic, D. , Jakovetic, D. , Kar, S.
Tackling heavy-tailed noise in distributed estimation: Asymptotic performance and tradeoffs
(2024) 2024 32nd Telecommunications Forum, TELFOR 2024 - Proceedings of Papers
Vukovic, M. , Jakovetic, D. , Bajovic, D.
NONLINEAR CONSENSUS+INNOVATIONS UNDER CORRELATED HEAVY-TAILED NOISES: MEAN SQUARE CONVERGENCE RATE AND ASYMPTOTICS
(2024) SIAM Journal on Control and Optimization
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