A tutorial on distributed (non-Bayesian) learning: Problem, algorithms and results

We overview some results on distributed learning with focus on a family of recently proposed algorithms known as non-Bayesian social learning. We consider different approaches to the distributed learning problem and its algorithmic solutions for the case of finitely many hypotheses. The original centralized problem is discussed at first, and then followed by a generalization to the distributed setting. The results on convergence and convergence rate are presented for both asymptotic and finite time regimes. Various extensions are discussed such as those dealing with directed time-varying networks, Nesterov's acceleration technique and a continuum sets of hypothesis.

[1]  Qipeng Liu,et al.  Distributed detection via Bayesian updates and consensus , 2014, 2015 34th Chinese Control Conference (CCC).

[2]  Nitin H. Vaidya,et al.  Defending non-Bayesian learning against adversarial attacks , 2018, Distributed Computing.

[3]  Yurii Nesterov,et al.  Primal-dual subgradient methods for convex problems , 2005, Math. Program..

[4]  Michael Athans,et al.  Convergence and asymptotic agreement in distributed decision problems , 1982, 1982 21st IEEE Conference on Decision and Control.

[5]  S. Venkatesh,et al.  Distributed Bayesian hypothesis testing in sensor networks , 2004, Proceedings of the 2004 American Control Conference.

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

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

[8]  Alexander Olshevsky.  Fast algorithms for distributed optimization and hypothesis testing: A tutorial , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[9]  Ali H. Sayed,et al.  Social Learning Over Weakly Connected Graphs , 2016, IEEE Transactions on Signal and Information Processing over Networks.

[10]  Angelia Nedic,et al.  Distributed learning with infinitely many hypotheses , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[11]  Saptarshi Bandyopadhyay,et al.  Distributed estimation using Bayesian consensus filtering , 2014, 2014 American Control Conference.

[12]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[13]  Theodoros Tsiligkaridis,et al.  Distributed probabilistic bisection search using social learning , 2017, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

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

[15]  Shahin Shahrampour,et al.  Learning without recall by random walks on directed graphs , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[16]  John N. Tsitsiklis,et al.  Convergence and asymptotic agreement in distributed decision problems , 1982 .

[17]  Aryeh Kontorovich,et al.  Concentration of measure without independence: a unified approach via the martingale method , 2016, ArXiv.

[18]  Aryan Mokhtari,et al.  Optimization in Dynamic Environments : Improved Regret Rates for Strongly Convex Problems , 2016 .

[19]  Angelia Nedic,et al.  Distributed Optimization Over Time-Varying Directed Graphs , 2015, IEEE Trans. Autom. Control..

[20]  Angelia Nedic,et al.  Network independent rates in distributed learning , 2015, 2016 American Control Conference (ACC).

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

[22]  Qipeng Liu,et al.  Non-Bayesian learning in social networks with time-varying weights , 2011, Proceedings of the 30th Chinese Control Conference.

[23]  Nitin H. Vaidya,et al.  Asynchronous Distributed Hypothesis Testing in the Presence of Crash Failures , 2016, ArXiv.

[24]  Michael I. Jordan,et al.  Ergodic mirror descent , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

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

[26]  Elchanan Mossel,et al.  Asymptotic learning on Bayesian social networks , 2012, Probability Theory and Related Fields.

[27]  Alvaro Sandroni,et al.  Non-Bayesian Updating: a Theoretical Framework , 2005 .

[28]  Ali H. Sayed,et al.  Diffusion social learning over weakly-connected graphs , 2016, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[29]  Shahin Shahrampour,et al.  Distributed Online Optimization in Dynamic Environments Using Mirror Descent , 2016, IEEE Transactions on Automatic Control.

[30]  Angelia Nedić,et al.  Fast Convergence Rates for Distributed Non-Bayesian Learning , 2015, IEEE Transactions on Automatic Control.

[31]  Alex Olshevsky,et al.  Linear Time Average Consensus on Fixed Graphs and Implications for Decentralized Optimization and Multi-Agent Control , 2014, 1411.4186.

[32]  Marc Teboulle,et al.  Mirror descent and nonlinear projected subgradient methods for convex optimization , 2003, Oper. Res. Lett..

[33]  Wang Xiaofan,et al.  Distributed detection via Bayesian updates and consensus , 2015, CCC 2015.

[34]  Zhongguo ke xue yuan.  Journal of systems science and complexity , 2001 .

[35]  Ali Jadbabaie,et al.  On consensus and exponentially fast social learning , 2012, 2012 American Control Conference (ACC).

[36]  Asuman E. Ozdaglar,et al.  Convergence of rule-of-thumb learning rules in social networks , 2008, 2008 47th IEEE Conference on Decision and Control.

[37]  H. Vincent Poor,et al.  Learning-Based Distributed Detection-Estimation in Sensor Networks With Unknown Sensor Defects , 2017, IEEE Transactions on Signal Processing.

[38]  Shahin Shahrampour,et al.  Switching to learn , 2015, 2015 American Control Conference (ACC).

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

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

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

[42]  Venkatesh Saligrama,et al.  Distributed Tracking in Multihop Sensor Networks With Communication Delays , 2007, IEEE Transactions on Signal Processing.

[43]  Lin Wang,et al.  Social learning with time-varying weights , 2014, Journal of Systems Science and Complexity.

[44]  Anit Kumar Sahu,et al.  Recursive Distributed Detection for Composite Hypothesis Testing: Algorithms and Asymptotics , 2016, ArXiv.

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

[46]  Alvaro Sandroni,et al.  Non-Bayesian Learning , 2010 .

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

[48]  M. Alanyali,et al.  Distributed Detection in Sensor Networks With Packet Losses and Finite Capacity Links , 2006, IEEE Transactions on Signal Processing.

[49]  J. Shamma,et al.  Belief consensus and distributed hypothesis testing in sensor networks , 2006 .