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.
We characterize the minimal global identifiability of the network for any consensus-based non-Bayesian learning to work.
Finite time convergence rate is obtained.
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.
KeywordsDistributed learning Crash failures Asynchrony
- 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
- 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
- 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.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
- 9.Molavi, P., Tahbaz-Salehi, A., Jadbabaie, A.: Foundations of non-Bayesian social learning. Columbia Business School Research Paper (2015)Google Scholar
- 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.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.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.Shahrampour, S., Rakhlin, A., Jadbabaie, A.: Distributed detection: finite-time analysis and impact of network topology (2014)Google Scholar
- 14.Shahrampour, S., Rakhlin, A., Jadbabaie, A.: Finite-time analysis of the distributed detection problem. CoRR, abs/1512.09311 (2015)Google Scholar
- 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
- 17.Tseng, L.: Fault-tolerant consensus and shared memory consistency model. Ph.D dissertation University of Illinois at Urbana-Champaign (2015)Google Scholar
- 18.Tsitsiklis, J.N.: Decentralized detection. In: Advances in Statistical Signal Processing, pp. 297–344. JAI Press (1993)Google Scholar