Randomized consensus algorithms over large scale networks

Abstract

Abstract-Suppose we have a directed graph G with set of nodes V = {1, . . . , N } and a measure x i for every node i ∈ V . The average consensus problem consists in computing the average x A = N −1 P i x i in an iterative way, exchanging information among nodes exclusively along the available edges in G. This problem appears in a number of different contexts since the 80's (decentralized computation, load balancing, clock syncronization) and, recently, has attracted much attention for possible applications to sensor networks (data fusion problems) and to coordinated control for mobile autonomous agents. Several algorithms for average consensus can be found in the literature: they differentiate on the basis of the amount of communication and computation they use, on their scalability with respect to the number of nodes, on their adaptability to time-varying graphs, and, finally, they can be deterministic or random. In this presentation we will focus on random algorithms: we will review some algorithms present in the literature and we will propose some new ones. We will present some performance results which will allow to make some comparison. Finally, we will establish some probabilistic concentration results which will give a stronger significance to previous results.

Convergence rate of the asymmetric Deffuant-Weisbuch dynamics

“…The communication of farmers is symmetric for this model. However, many social networks, such as the social network on the Internet [7] and the robot network [8] , are asymmetric.…”

“…In fact, various previous theoretical convergence rate results of multi-agent systems are obtained [8,[13][14][15][16] . In these works, [8] and [13] obtained that if all system matrices are doubly stochastic, then the system convergence rate is negative exponential. In [16], negative power time convergence rate was studied for the multi-agent system with state-independent time-varying topology.…”

Spread of (mis)information in social networks

“…In addition to the papers on learning mentioned above, our paper is related to work on consensus, which is motivated by different problems, but typically leads to a similar mathematical formulation (Tsitsiklis, 1984;Tsitsiklis et al, 1986;Jadbabaie et al, 2003;Olfati-Saber and Murray, 2004;Olshevsky and Tsitsiklis, forthcoming;Nedić and Ozdaglar, forthcoming;Fagnani and Zampieri, forthcoming). In consensus problems, the focus is on whether the beliefs or the values held by different units (which might correspond to individuals, sensors or distributed processors) converge to a common value.…”

Opinion Dynamics and Learning in Social Networks

“…Hence, at each time instance agents update their beliefs to a convex combination of their current beliefs and the beliefs of their neighbors. 12 10 The DeGroot model and variations have also been studied extensively in the cooperative control literature as natural algorithms for achieving cooperative behavior with local information in networked-systems (see [18,33,62,67,71,72,[87][88][89]). 11 The appealing interpretation is that this type of averaging would be optimal at time t = 0 if all agents had independent beliefs drawn from a normal distribution with mean equal to the underlying state and weights adjusted according to the precision of the distribution.…”