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Non-Bayesian Learning in the Presence of Byzantine Agents

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Distributed Computing (DISC 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9888))

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Abstract

This paper addresses the problem of non-Bayesian learning over multi-agent networks, where agents repeatedly collect partially informative observations about an unknown state of the world, and try to collaboratively learn the true state. We focus on the impact of the Byzantine agents on the performance of consensus-based non-Bayesian learning. Our goal is to design an algorithm for the non-faulty agents to collaboratively learn the true state through local communication.

We propose an update rule wherein each agent updates its local beliefs as (up to normalization) the product of (1) the likelihood of the cumulative private signals and (2) the weighted geometric average of the beliefs of its incoming neighbors and itself (using Byzantine consensus). Under mild assumptions on the underlying network structure and the global identifiability of the network, we show that all the non-faulty agents asymptotically agree on the true state almost surely.

This research is supported in part by National Science Foundation awards NSF 1329681 and 1421918. Any opinions, findings, and conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the funding agencies or the U.S. government.

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Notes

  1. 1.

    In this paper, every vector considered is a column vector.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Champaign, USA

    Lili Su & Nitin H. Vaidya

Authors
  1. Lili Su
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  2. Nitin H. Vaidya
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Correspondence to Lili Su .

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Editors and Affiliations

  1. LABRI, Univ of Bordeaux LABRI, Talence Cedex, France

    Cyril Gavoille

  2. CNRS, Universite Bordeaux 1 CNRS, Talence Cedex, France

    David Ilcinkas

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Su, L., Vaidya, N.H. (2016). Non-Bayesian Learning in the Presence of Byzantine Agents. In: Gavoille, C., Ilcinkas, D. (eds) Distributed Computing. DISC 2016. Lecture Notes in Computer Science(), vol 9888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53426-7_30

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  • DOI: https://doi.org/10.1007/978-3-662-53426-7_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-53425-0

  • Online ISBN: 978-3-662-53426-7

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