Social learning with time-varying weights

Liu, Qipeng; Fang, Aili; Wang, Lin; Wang, Xiaofan

doi:10.1007/s11424-014-1195-0

Cited by 26 publications

(25 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recall from the previous section that replacing IIA with separability results in a learning rule according to which agent i linearly combines the beliefs of her neighbors j ∈ N i with weights a ijt > 0. Our next result, which generalizes the main result of Jadbabaie et al (2012) and proves a conjecture of Liu et al (2014), characterizes the conditions under which such a learning rule leads to the long-run aggregation of information.…”

Section: Degroot Learningsupporting

confidence: 64%

See 1 more Smart Citation

A Theory of Non-Bayesian Social Learning

2018

View full text Add to dashboard Cite

This paper studies the behavioral foundations of non‐Bayesian models of learning over social networks and develops a taxonomy of conditions for information aggregation in a general framework. As our main behavioral assumption, we postulate that agents follow social learning rules that satisfy “imperfect recall,” according to which they treat the current beliefs of their neighbors as sufficient statistics for the entire history of their observations. We augment this assumption with various restrictions on how agents process the information provided by their neighbors and obtain representation theorems for the corresponding learning rules (including the canonical model of DeGroot). We then obtain general long‐run learning results that are not tied to the learning rules' specific functional forms, thus identifying the fundamental forces that lead to learning, non‐learning, and mislearning in social networks. Our results illustrate that, in the presence of imperfect recall, long‐run aggregation of information is closely linked to (i) the rate at which agents discount their neighbors' information over time, (ii) the curvature of agents' social learning rules, and (iii) whether their initial tendencies are amplified or moderated as a result of social interactions.

show abstract

Section: Degroot Learningsupporting

confidence: 64%

“…To establish (31), we follow an approach similar to Liu et al (2014). Applying part (d) of Lemma A.2 to (28) implies that…”

Section: Proof Of Theoremmentioning

confidence: 99%

A Theory of Non-Bayesian Social Learning

2018

View full text Add to dashboard Cite

show abstract

“…We emphasize that the proposed learning rule given by Algorithm 1 does not employ any form of "belief-averaging". This feature is in stark contrast with existing approaches to distributed hypothesis testing that rely either on linear opinion pooling [4][5][6], or log-linear opinion pooling [7][8][9][10][11][12][13][14]. As such, the lack of linearity in our belief update rule precludes (direct or indirect) adaptation of existing analysis techniques to suit our needs.…”

mentioning

confidence: 92%

“…Notably, finite-time concentration results are derived in [9][10][11], and a large-deviation analysis is conducted in [12,13] for a broad class of distributions that generate the agents' observation profiles. Extensions to different types of time-varying graphs have also been considered in [6,[8][9][10][11]. In a recent paper [15], the authors go beyond specific functional forms of belief-update rules and, instead, adopt an axiomatic framework that identifies the fundamental factors responsible for social learning.…”

Section: Introductionmentioning

confidence: 99%

A New Approach for Distributed Hypothesis Testing with Extensions to Byzantine-Resilience

Mitra¹,

Richards

Sundaram³

2019

2019 American Control Conference (ACC)

View full text Add to dashboard Cite

We study a setting where a group of agents, each receiving partially informative private signals, seek to collaboratively learn the true underlying state of the world (from a finite set of hypotheses) that generates their joint observation profiles. To solve this problem, we propose a distributed learning rule that differs fundamentally from existing approaches, in that it does not employ any form of "belief-averaging". Instead, agents update their beliefs based on a min-rule. Under standard assumptions on the observation model and the network structure, we establish that each agent learns the truth asymptotically almost surely. As our main contribution, we prove that with probability 1, each false hypothesis is ruled out by every agent exponentially fast at a network-independent rate that is strictly larger than existing rates. We then develop a computationally-efficient variant of our learning rule that is provably resilient to agents who do not behave as expected (as represented by a Byzantine adversary model) and deliberately try to spread misinformation.

show abstract

“…In social learning models, individuals engage in communication with their neighbors in order to learn from their experiences. For more details, we refer readers to see [7]- [9]. A large amount of papers concerning consensus algorithms have been published [10], [11], [12], [13], [14], most of which focused on the average principle,i.e., the current state of each agent is an average of the previous states of its own and its neighbors, which is implemented by communication between agents and can be described by the following difference equations for the discrete-time cases:…”

Section: Introductionmentioning

confidence: 99%

Cluster Consensus in Discrete-Time Networks of Multiagents With Inter-Cluster Nonidentical Inputs

Han¹,

Lu²,

Chen³

2013

IEEE Trans. Neural Netw. Learning Syst.

115

View full text Add to dashboard Cite

Abstract-In this paper, cluster consensus of multi-agent systems is studied via inter-cluster nonidentical inputs. Here, we consider general graph topologies, which might be time-varying. The cluster consensus is defined by two aspects: the intracluster synchronization, that the state differences between each pair of agents in the same cluster converge to zero, and intercluster separation, that the states of the agents in different clusters are separated. For intra-cluster synchronization, the concepts and theories of consensus including the spanning trees, scramblingness, infinite stochastic matrix product and Hajnal inequality, are extended. With them, it is proved that if the graph has cluster spanning trees and all vertices self-linked, then static linear system can realize intra-cluster synchronization. For the time-varying coupling cases, it is proved that if there exists T > 0 such that the union graph across any T -length time interval has cluster spanning trees and all graphs has all vertices self-linked, then the time-varying linear system can also realize intra-cluster synchronization. Under the assumption of common inter-cluster influence, a sort of inter-cluster nonidentical inputs are utilized to realize inter-cluster separation, that each agent in the same cluster receives the same inputs and agents in different clusters have different inputs. In addition, the boundedness of the infinite sum of the inputs can guarantee the boundedness of the trajectory. As an application, we employ a modified nonBayesian social learning model to illustrate the effectiveness of our results.

show abstract

Social learning with time-varying weights

Cited by 26 publications

References 15 publications

A Theory of Non-Bayesian Social Learning

A Theory of Non-Bayesian Social Learning

A New Approach for Distributed Hypothesis Testing with Extensions to Byzantine-Resilience

Cluster Consensus in Discrete-Time Networks of Multiagents With Inter-Cluster Nonidentical Inputs

Contact Info

Product

Resources

About