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Convergence speed in distributed consensus and averaging
 IN PROC. OF THE 45TH IEEE CDC
, 2006
"... We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove ..."
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Cited by 138 (4 self)
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We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove lower bounds on the worstcase convergence time for various classes of linear, timeinvariant, distributed consensus methods, and provide an algorithm that essentially matches those lower bounds. We then consider the case of a timevarying topology, and provide a polynomialtime averaging algorithm.
OPINION FLUCTUATIONS AND DISAGREEMENT IN SOCIAL NETWORKS
 SUBMITTED TO THE ANNALS OF APPLIED PROBABILITY
, 2010
"... We study a stochastic gossip model of continuous opinion dynamics in a society consisting of two types of agents: regular agents, who update their beliefs according to information that they receive from their social neighbors; and stubborn agents, who never update their opinions and might represent ..."
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Cited by 26 (5 self)
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We study a stochastic gossip model of continuous opinion dynamics in a society consisting of two types of agents: regular agents, who update their beliefs according to information that they receive from their social neighbors; and stubborn agents, who never update their opinions and might represent leaders, political parties or media sources attempting to influence the beliefs in the rest of the society. When the society contains stubborn agents with different opinions, opinion dynamics never lead to a consensus (among the regular agents). Instead, beliefs in the society almost surely fail to converge, and the belief of each regular agent converges in law to a nondegenerate random variable. The model thus generates longrun disagreement and continuous opinion fluctuations. The structure of the social network and the location of stubborn agents within it shape opinion dynamics. When the society is “highly fluid”, meaning that the mixing time of the random walk on the graph describing the social network is small relative to (the inverse of) the relative size of the linkages to stubborn agents, the ergodic beliefs of most of the agents concentrate around a certain common value. We also show that under additional conditions, the ergodic beliefs distribution becomes “approximately chaotic”, meaning that the variance of the aggregate belief of the society vanishes in the large population limit while individual opinions still fluctuate significantly.
NonBayesian Social Learning
, 2011
"... We develop a dynamic model of opinion formation in social networks when the information required for learning a payoffrelevant parameter may not be at the disposal of any single agent. Individuals engage in communication with their neighbors in order to learn from their experiences. However, instea ..."
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Cited by 25 (6 self)
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We develop a dynamic model of opinion formation in social networks when the information required for learning a payoffrelevant parameter may not be at the disposal of any single agent. Individuals engage in communication with their neighbors in order to learn from their experiences. However, instead of incorporating the views of their neighbors in a fully Bayesian manner, agents use a simple updating rule which linearly combines their personal experience and the views of their neighbors (even though the neighbors ’ views may be quite inaccurate). This nonBayesian learning rule is motivated by the formidable complexity required to fully implement Bayesian updating in networks. We show that, as long as individuals take their personal signals into account in a Bayesian way, repeated interactions lead them to successfully aggregate information and learn the true underlying state of the world. This result holds in spite of the apparent naïveté of agents’ updating rule, the agents ’ need for information from sources the existence of which they may not be aware of, the possibility that the most persuasive agents in the network are precisely those least informed and with worst prior views, and the assumption that no agent can
Distributed MultiAgent Optimization with StateDependent Communication
, 2010
"... We study distributed algorithms for solving global optimization problems in which the objective function is the sum of local objective functions of agents and the constraint set is given by the intersection of local constraint sets of agents. We assume that each agent knows only his own local obje ..."
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Cited by 23 (2 self)
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We study distributed algorithms for solving global optimization problems in which the objective function is the sum of local objective functions of agents and the constraint set is given by the intersection of local constraint sets of agents. We assume that each agent knows only his own local objective function and constraint set, and exchanges information with the other agents over a randomly varying network topology to update his information state. We assume a statedependent communication model over this topology: communication is Markovian with respect to the states of the agents and the probability with which the links are available depends on the states of the agents. In this paper, we study a projected multiagent subgradient algorithm under statedependent communication. The algorithm involves each agent performing a local averaging to combine his estimate with the other agents’ estimates, taking a subgradient step along his local objective function, and projecting the estimates
Opinion fluctuations and persistent disagreement in social networks
 in Decision and Control and European Control Conference (CDCECC), 2011 50th IEEE Conference on. IEEE, 2011
"... Abstract — Disagreement among individuals in a society, even on central questions that have been debated for centuries, is the rule; agreement is the rare exception. How can disagreement of this sort persist for so long? Most existing models of communication and learning, based on Bayesian or nonB ..."
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Cited by 13 (1 self)
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Abstract — Disagreement among individuals in a society, even on central questions that have been debated for centuries, is the rule; agreement is the rare exception. How can disagreement of this sort persist for so long? Most existing models of communication and learning, based on Bayesian or nonBayesian updating mechanisms, typically lead to consensus provided that communication takes place over a strongly connected network. These models are thus unable to explain persistent disagreements, and belief fluctuations. We propose a tractable model that generates longrun disagreements and persistent opinion fluctuations. Our model involves a stochastic gossip model of continuous opinion dynamics in a society consisting of two types of agents: regular agents, who update their beliefs according to information that they receive from their social neighbors; and stubborn agents, who never update their opinions and might represent leaders, political parties or media sources attempting to influence the beliefs in the rest of the society. When the society contains stubborn agents with different opinions, the belief dynamics never lead to a consensus (among the regular agents). Instead, beliefs in the society almost surely fail to converge, the belief profile keeps on oscillating in an ergodic fashion, and it converges in law to a nondegenerate random vector. The structure of the graph describing the social network and the location of stubborn agents within it shape the long run behavior of the opinion dynamics. We prove that, when the society is highly fluid, meaning that the mixing time of the random walk on the graph describing the social network is small relative to the inverse of the relative size of the linkages to stubborn agents, a condition of homogeneous influence emerges, whereby the ergodic beliefs of most of the regular agents have approximately equal marginal distributions. This clearly need not imply approximate consensus and in fact we show, under mild conditions, the ergodic belief distribution becomes approximately chaotic, meaning that the variance of the aggregate belief of the society vanishes in the large population limit while individual opinions still fluctuate significantly in an essentially uncorrelated way. I.
Estimation of Causal Peer Influence Effects
"... The broad adoption of social media has generated interest in leveraging peer influence for inducing desired user behavior. Quantifying the causal effect of peer influence presents technical challenges, however, including how to deal with social interference, complex response functions and network un ..."
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Cited by 6 (0 self)
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The broad adoption of social media has generated interest in leveraging peer influence for inducing desired user behavior. Quantifying the causal effect of peer influence presents technical challenges, however, including how to deal with social interference, complex response functions and network uncertainty. In this paper, we extend potential outcomes to allow for interference, we introduce welldefined causal estimands of peerinfluence, and we develop two estimation procedures: a frequentist procedure relying on a sequential randomization design that requires knowledge of the network but operates under complicated response functions, and a Bayesian procedure which accounts for network uncertainty but relies on a linear response assumption to increase estimation precision. Our results show the advantages and disadvantages of the proposed methods in a number of situations. 1.
How agreement and disagreement evolve over random dynamic networks
 IEEE J. on Selected Area in Communications
, 2013
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On new characterizations of social influence in social networks
 in Proceedings of the 2013 American Control Conference, 2013
"... Abstract — We propose new characterizations of social influence, which quantify both the transient and the steadystate propagation of beliefs across society. These characterizations are used to optimally choose a desired number of agents in a social network to serve as social leaders with maximal ..."
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Cited by 4 (3 self)
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Abstract — We propose new characterizations of social influence, which quantify both the transient and the steadystate propagation of beliefs across society. These characterizations are used to optimally choose a desired number of agents in a social network to serve as social leaders with maximal social impact. We then consider a framework for optimally creating new social links subject to resource constraints, in order to improve the influence of designated agents or social leaders. We show that the formulated optimization problems are convex with respect to the individual elements of the optimization variables. This motivates the use of the coordinate descent method, a simple but efficient algorithm wellsuited to largescale optimization problems. Finally, using demonstrative examples, we compare the ability of our proposed characterizations of social influence in identifying the most influential agents with that of other measures of influence developed in the social networks literature. Index Terms — Betweenness centrality, consensus, convex relaxation, coordinate descent, leader selection, optimization,
On asymptotic consensus value in directed random networks
 in 49th IEEE Conference on Decision and Control
, 2010
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