Asynchronous Non-Bayesian Learning in the Presence of Crash Failures

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10083)

Abstract

This paper addresses the problem of non-Bayesian learning in multi-agent networks, where agents repeatedly collect local observations about an unknown state of the world, and try to collaboratively detect the true state through information exchange. We focus on the impact of failures and asynchrony – two fundamental factors in distributed systems – on the performance of consensus-based non-Bayesian learning. In particular, we assume the networked agents may suffer crash faults, and messages delay can be arbitrarily long but finite.

  1. 1.

    We characterize the minimal global identifiability of the network for any consensus-based non-Bayesian learning to work.

     
  2. 2.

    Finite time convergence rate is obtained.

     
  3. 3.

    As part of our convergence analysis, we obtain a generalization of a celebrated result by Wolfowitz and Hajnal to submatrices, which might be of independent interest.

     

Keywords

Distributed learning Crash failures Asynchrony 

References

  1. 1.
    Chamberland, J.-F., Veeravalli, V.V.: Decentralized detection in sensor networks. IEEE Trans. Signal Process. 51(2), 407–416 (2003)CrossRefGoogle Scholar
  2. 2.
    Feldman, M., Immorlica, N., Lucier, B., Weinberg, S.M.: Reaching consensus via non-Bayesian asynchronous learning in social networks. CoRR, abs/1408.5192 (2014)Google Scholar
  3. 3.
    Gale, D., Kariv, S.: Bayesian learning in social networks. Games Econ. Behav. 45(2), 329–346 (2003)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Hajnal, J., Bartlett, M.: Weak ergodicity in non-homogeneous Markov chains. In: Mathematical Proceedings of the Cambridge Philosophical Society, vol. 54, pp. 233–246. Cambridge Univ Press (1958)Google Scholar
  5. 5.
    Jadbabaie, A., Molavi, P., Sandroni, A., Tahbaz-Salehi, A.: Non-Bayesian social learning. Games Econ. Behav. 76(1), 210–225 (2012)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Jadbabaie, A., Molavi, P., Tahbaz-Salehi, A.: Information heterogeneity and the speed of learning in social networks. Columbia Business School Research Paper, (13–28) (2013)Google Scholar
  7. 7.
    Lalitha, A., Sarwate, A., Javidi, T.: Social learning and distributed hypothesis testing. In: IEEE International Symposium on Information Theory, pp. 551–555. IEEE (2014)Google Scholar
  8. 8.
    Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann, San Francisco (1996)MATHGoogle Scholar
  9. 9.
    Molavi, P., Tahbaz-Salehi, A., Jadbabaie, A.: Foundations of non-Bayesian social learning. Columbia Business School Research Paper (2015)Google Scholar
  10. 10.
    Nedić, A., Olshevsky, A., Uribe, C.A.: Nonasymptotic convergence rates for cooperative learning over time-varying directed graphs. In: American Control Conference (ACC), pp. 5884–5889. IEEE (2015)Google Scholar
  11. 11.
    Rad, K.R., Tahbaz-Salehi, A.: Distributed parameter estimation in networks. In: 49th IEEE Conference on Decision and Control (CDC), pp. 5050–5055. IEEE (2010)Google Scholar
  12. 12.
    Shahrampour, S., Jadbabaie, A.: Exponentially fast parameter estimation in networks using distributed dual averaging. In: 52nd IEEE Conference on Decision and Control, pp. 6196–6201. IEEE (2013)Google Scholar
  13. 13.
    Shahrampour, S., Rakhlin, A., Jadbabaie, A.: Distributed detection: finite-time analysis and impact of network topology (2014)Google Scholar
  14. 14.
    Shahrampour, S., Rakhlin, A., Jadbabaie, A.: Finite-time analysis of the distributed detection problem. CoRR, abs/1512.09311 (2015)Google Scholar
  15. 15.
    Su, L., Vaidya, N.H.: Asynchronous distributed hypothesis testing in the presence of crash failures. University of Illinois at Urbana-Champaign, Technical report (2016)Google Scholar
  16. 16.
    Su, L., Vaidya, N.H.: Non-Bayesian learning in the presence of Byzantine agents. In: Gavoille, C., Ilcinkas, D. (eds.) DISC 2016. LNCS, vol. 9888, pp. 414–427. Springer, Heidelberg (2016). doi:10.1007/978-3-662-53426-7_30 CrossRefGoogle Scholar
  17. 17.
    Tseng, L.: Fault-tolerant consensus and shared memory consistency model. Ph.D dissertation University of Illinois at Urbana-Champaign (2015)Google Scholar
  18. 18.
    Tsitsiklis, J.N.: Decentralized detection. In: Advances in Statistical Signal Processing, pp. 297–344. JAI Press (1993)Google Scholar
  19. 19.
    Varshney, P.K.: Distributed Bayesian detection: parallel fusion network. Distributed Detection and Data Fusion, pp. 36–118. Springer, New York (1997)CrossRefGoogle Scholar
  20. 20.
    Wolfowitz, J.: Products of indecomposable, aperiodic, stochastic matrices. Proc. Am. Math. Soc. 14(5), 733–737 (1963)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Wong, E., Hajek, B.: Stochastic Processes in Engineering Systems. Springer Science & Business Media, New York (2012)MATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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