Social Learning With Bayesian Agents and Random Decision Making

In this paper, we study the effect of randomness in the decision making of agents on social learning. In the addressed system, the agents make decisions sequentially about the true state of nature. Each agent observes a signal produced according to one of two hypotheses, which represents the state of nature. The signals of all the agents are generated independently from the same state. The agents also know the decisions of all the previous agents in the network. The randomness in this paper is modeled by a policy that amounts to random mapping of the beliefs of the agents to the action space. We propose that the agents learn from the decisions of the previous agents and update their beliefs by using the Bayesian theory. We define the concept of social belief about the truthfulness of the two hypotheses and provide results on the convergence of the social belief. We also prove that with the proposed random policy, information cascade can be avoided and asymptotic learning occurs. We apply the random policy to data models that represent the observations by a distribution belonging to the exponential family. We then provide performance and convergence analysis of the proposed method as well as simulation results that include comparisons with deterministic and hybrid policies.

[1]  Vikram Krishnamurthy,et al.  A Tutorial on Interactive Sensing in Social Networks , 2014, IEEE Transactions on Computational Social Systems.

[2]  K. J. Ray Liu,et al.  Sequential Chinese Restaurant Game , 2013, IEEE Transactions on Signal Processing.

[3]  S. Bikhchandani,et al.  You have printed the following article : A Theory of Fads , Fashion , Custom , and Cultural Change as Informational Cascades , 2007 .

[4]  Petar M. Djuric,et al.  Distributed Bayesian learning in multiagent systems: Improving our understanding of its capabilities and limitations , 2012, IEEE Signal Processing Magazine.

[5]  H. Vincent Poor,et al.  Social learning and bayesian games in multiagent signal processing: how do local and global decision makers interact? , 2013, IEEE Signal Processing Magazine.

[6]  Lones Smith,et al.  Pathological Outcomes of Observational Learning , 2000 .

[7]  Anna Scaglione,et al.  Models for the Diffusion of Beliefs in Social Networks: An Overview , 2013, IEEE Signal Processing Magazine.

[8]  T. Cover.  Hypothesis Testing with Finite Statistics , 1969 .

[9]  Matthew O. Jackson,et al.  Naïve Learning in Social Networks and the Wisdom of Crowds , 2010 .

[10]  M. Athans,et al.  Distributed detection by a large team of sensors in tandem , 1992 .

[11]  Jack Koplowitz,et al.  Necessary and sufficient memory size for m-hypothesis testing , 1975, IEEE Trans. Inf. Theory.

[12]  Petar M. Djuric,et al.  Sequential Bayesian learning in linear networks with random decision making , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[13]  Alejandro Ribeiro,et al.  Bayesian Quadratic Network Game Filters , 2013, IEEE Transactions on Signal Processing.

[14]  Edwin K. P. Chong,et al.  This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. 1 Hypothesis Testing in Feedforward Networks with Broadcast Failures , 2022 .

[15]  Vikram Krishnamurthy,et al.  Bayesian Sequential Detection With Phase-Distributed Change Time and Nonlinear Penalty—A POMDP Lattice Programming Approach , 2011, IEEE Transactions on Information Theory.

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

[17]  C. Chamley.  Rational Herds: Economic Models of Social Learning , 2003 .

[18]  Petar M. Djuric,et al.  A Gossip Method for Optimal Consensus on a Binary State From Binary Actions , 2013, IEEE Journal of Selected Topics in Signal Processing.

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

[20]  Pramod K Varshney,et al.  Distributed inference in wireless sensor networks , 2012, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[21]  X. Vives.  Learning from others: A welfare analysis , 1997 .

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

[23]  A. Banerjee,et al.  A Simple Model of Herd Behavior , 1992 .

[24]  John N. Tsitsiklis,et al.  On Learning With Finite Memory , 2012, IEEE Transactions on Information Theory.

[25]  Alejandro Ribeiro,et al.  Learning in network games with incomplete information: asymptotic analysis and tractable implementation of rational behavior , 2013, IEEE Signal Processing Magazine.

[26]  P. F. Swaszek,et al.  On the performance of serial networks in distributed detection , 1993 .

[27]  Samir Ranjan Das,et al.  Serial data fusion using space-filling curves in wireless sensor networks , 2004, 2004 First Annual IEEE Communications Society Conference on Sensor and Ad Hoc Communications and Networks, 2004. IEEE SECON 2004..