Asynchronous Non-Bayesian Learning in the Presence of Crash Failures

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]  M. Bartlett,et al.  Weak ergodicity in non-homogeneous Markov chains , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  T. Javidi,et al.  Social learning and distributed hypothesis testing , 2014, 2014 IEEE International Symposium on Information Theory.

[3]  Pramod K. Varshney,et al.  Distributed Bayesian Detection: Parallel Fusion Network , 1997 .

[4]  Nitin H. Vaidya,et al.  Non-Bayesian Learning in the Presence of Byzantine Agents , 2016, DISC.

[5]  Pooya Molavi,et al.  Foundations of Non-Bayesian Social Learning , 2016 .

[6]  Pooya Molavi,et al.  Information Heterogeneity and the Speed of Learning in Social Networks , 2013 .

[7]  Venugopal V. Veeravalli,et al.  Decentralized detection in sensor networks , 2003, IEEE Trans. Signal Process..

[8]  Nikhil R. Devanur,et al.  Reaching Consensus via Non-Bayesian Asynchronous Learning in Social Networks , 2014, APPROX-RANDOM.

[9]  E. Wong,et al.  Stochastic Processes in Engineering Systems , 1984 .

[10]  Kamiar Rahnama Rad,et al.  Distributed parameter estimation in networks , 2010, 49th IEEE Conference on Decision and Control (CDC).

[11]  J. Wolfowitz.  Products of indecomposable, aperiodic, stochastic matrices , 1963 .

[12]  Ali Jadbabaie,et al.  Non-Bayesian Social Learning , 2011, Games Econ. Behav..

[13]  Shahin Shahrampour,et al.  Finite-time analysis of the distributed detection problem , 2015, 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[14]  Douglas Gale,et al.  Bayesian learning in social networks , 2003, Games Econ. Behav..

[15]  Angelia Nedic,et al.  Nonasymptotic convergence rates for cooperative learning over time-varying directed graphs , 2014, 2015 American Control Conference (ACC).

[16]  Shahin Shahrampour,et al.  Distributed Detection: Finite-Time Analysis and Impact of Network Topology , 2014, IEEE Transactions on Automatic Control.

[17]  Shahin Shahrampour,et al.  Exponentially fast parameter estimation in networks using distributed dual averaging , 2013, 52nd IEEE Conference on Decision and Control.

[18]  Nancy A. Lynch,et al.  Distributed Algorithms , 1992, Lecture Notes in Computer Science.