Fast convergence of quantized consensus using Metropolis chains

Başary, Tamer; Etesami, S. Rasoul; Olshevsky, Alex

doi:10.1109/cdc.2014.7039566

Cited by 12 publications

(7 citation statements)

References 20 publications

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“…Proof of Theorem 2: The system (27) can be viewed as a linear consensus system with input u(t) = ∆z(t) v(t) and C(t) = I. Recall the definition of Φ(t, τ ) in (21), we can write the output as…”

Section: Proof Of Theoremmentioning

confidence: 99%

Distributed learning of average belief over networks using sequential observations

Zhang

Liu

et al. 2020

Automatica

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This paper addresses the problem of distributed learning of average belief with sequential observations, in which a network of n > 1 agents aim to reach a consensus on the average value of their beliefs, by exchanging information only with their neighbors. Each agent has sequentially arriving samples of its belief in an online manner. The neighbor relationships among the n agents are described by a graph which is possibly time-varying, whose vertices correspond to agents and whose edges depict neighbor relationships. Two distributed online algorithms are introduced for undirected and directed graphs, which are both shown to converge to the average belief almost surely. Moreover, the sequences generated by both algorithms are shown to reach consensus with an O(1/t) rate with high probability, where t is the number of iterations. For undirected graphs, the corresponding algorithm is modified for the case with quantized communication and limited precision of the division operation. It is shown that the modified algorithm causes all n agents to either reach a quantized consensus or enter a small neighborhood around the average of their beliefs. Numerical simulations are then provided to corroborate the theoretical results.

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Section: Proof Of Theoremmentioning

confidence: 99%

Distributed learning of average belief over networks using sequential observations

Zhang

Liu

et al. 2020

Automatica

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“…Given a network G(t) at time t ≥ 0, we associate a Poisson process with each edge {i, j} of G(t) with a rate of λ ij (t) = 1/ max(d i (t), d j (t)), i.e., the Metropolis weight corresponding to that edge at time t. When an edge {i, j} ∈ E(t) registers an arrival, we let the incident nodes update their values based on (2). Moreover, for each node x and time t, the self-loop (x, x) registers arrivals according to a Poisson process with rate of…”

Section: A Quantized Metropolis Model Over Time-varying Networkmentioning

confidence: 99%

Convergence Time of Quantized Metropolis Consensus Over Time-Varying Networks

Başar

Etesami

Olshevsky

2016

IEEE Trans. Automat. Contr.

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We consider the quantized consensus problem on undirected time-varying connected graphs with n nodes, and devise a protocol with fast convergence time to the set of consensus points. Specifically, we show that when the edges of each network in a sequence of connected time-varying networks are activated based on Poisson processes with Metropolis rates, the expected convergence time to the set of consensus points is at most O(n 2 log 2 n), where each node performs a constant number of updates per unit time.

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“…time of this process depends upon the meeting time of two random walkers in a graph and has received a significant attention in [10,11,12] among others. When considering heterogeneous execution speed, methods developed for the homogeneous case may fail to converge to the desired convergence set.…”

Section: Introductionmentioning

confidence: 99%

Gossip based asynchronous and randomized distributed task assignment with guaranteed performance on heterogeneous networks

Franceschelli

Giua

Seatzu

2017

Nonlinear Analysis: Hybrid Systems

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The main contribution of this paper is a novel distributed algorithm based on asynchronous and randomized local interactions, i.e., gossip based, for task assignment on heterogeneous networks. We consider a set of tasks with heterogeneous cost to be assigned to a set of nodes with heterogeneous execution speed and interconnected by a network with unknown topology represented by an undirected graph. Our objective is to minimize the execution time of the set of tasks by the networked system. We propose a local interaction rule which allows the nodes of a network to cooperatively assign tasks among themselves with a guaranteed performance with respect to the optimal assignment exploiting a gossip based randomized interaction scheme. We first characterize the convergence properties of the proposed approach, then we propose an edge selection process and a distributed embedded stop criterion to terminate communications, not only task exchanges, while keeping the performance guarantee. Numerical simulations are finally presented to corroborate the theoretical results.

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Fast convergence of quantized consensus using Metropolis chains

Cited by 12 publications

References 20 publications

Distributed learning of average belief over networks using sequential observations

Distributed learning of average belief over networks using sequential observations

Convergence Time of Quantized Metropolis Consensus Over Time-Varying Networks

Gossip based asynchronous and randomized distributed task assignment with guaranteed performance on heterogeneous networks

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