Results 1  10
of
24
Broadcast gossip algorithms for consensus
 IEEE Trans. Signal Process
, 2009
"... Abstract—Motivated by applications to wireless sensor, peertopeer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and computing in an arbitrarily connected network of nodes. Specifically, we study a broadcastingbased gossiping algorithm to compute th ..."
Abstract

Cited by 95 (6 self)
 Add to MetaCart
Abstract—Motivated by applications to wireless sensor, peertopeer, and ad hoc networks, we study distributed broadcasting algorithms for exchanging information and computing in an arbitrarily connected network of nodes. Specifically, we study a broadcastingbased gossiping algorithm to compute the (possibly weighted) average of the initial measurements of the nodes at every node in the network. We show that the broadcast gossip algorithm converges almost surely to a consensus. We prove that the random consensus value is, in expectation, the average of initial node measurements and that it can be made arbitrarily close to this value in mean squared error sense, under a balanced connectivity model and by trading off convergence speed with accuracy of the computation. We provide theoretical and numerical results on the mean square error performance, on the convergence rate and study the effect of the “mixing parameter ” on the convergence rate of the broadcast gossip algorithm. The results indicate that the mean squared error strictly decreases through iterations until the consensus is achieved. Finally, we assess and compare the communication cost of the broadcast gossip algorithm to achieve a given distance to consensus through theoretical and numerical results. Index Terms—Broadcasting, distributed average consensus, gossip algorithms, sensor networks. I.
A distributed newton method for network utility maximization
, 2010
"... Abstract — Most existing work uses dual decomposition and subgradient methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This work develops an alternative distributed Newtontype fast converging algorithm for s ..."
Abstract

Cited by 37 (5 self)
 Add to MetaCart
(Show Context)
Abstract — Most existing work uses dual decomposition and subgradient methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This work develops an alternative distributed Newtontype fast converging algorithm for solving network utility maximization problems with selfconcordant utility functions. By using novel matrix splitting techniques, both primal and dual updates for the Newton step can be computed using iterative schemes in a decentralized manner with limited information exchange. Similarly, the stepsize can be obtained via an iterative consensusbased averaging scheme. We show that even when the Newton direction and the stepsize in our method are computed within some error (due to finite truncation of the iterative schemes), the resulting objective function value still converges superlinearly to an explicitly characterized error neighborhood. Simulation results demonstrate significant convergence rate improvement of our algorithm relative to the existing subgradient methods based on dual decomposition. I.
Distributed consensus over network with noisy links
 in Proceedings of the 12th International Conference on Information Fusion, 2009
"... Abstract – We consider a distributed consensus problem where a set of agents want to agree on a common value through local computations and communications. We assume that agents communicate over a network with timevarying topology and noisy communication links. We are interested in the case when t ..."
Abstract

Cited by 13 (4 self)
 Add to MetaCart
(Show Context)
Abstract – We consider a distributed consensus problem where a set of agents want to agree on a common value through local computations and communications. We assume that agents communicate over a network with timevarying topology and noisy communication links. We are interested in the case when the link noise is independent in time, and it has zero mean and bounded variance. We present and study an iterative algorithm with a diminishing stepsize. We show that the algorithm converges in expectation and almost surely to a “random ” consensus, and we characterize the statistics of the consensus. In particular, we give the expected value of the consensus and provide an upper bound on its variance.
Distributed consensus and optimization under communication delays
 in 49th Allerton
, 2011
"... Abstract—We study the effects of communication delays in distributed consensus and optimization algorithms. We propose two ways to model delays. First, assuming each edge of a communication network has a fixed delay, we characterize the consensus value exactly as a function of the delays and edge we ..."
Abstract

Cited by 11 (2 self)
 Add to MetaCart
(Show Context)
Abstract—We study the effects of communication delays in distributed consensus and optimization algorithms. We propose two ways to model delays. First, assuming each edge of a communication network has a fixed delay, we characterize the consensus value exactly as a function of the delays and edge weights and obtain convergence rate bounds using results from nonreversible Markov chains. Second, we propose a novel way to model random delays per edge. Our model allows the reception of multiple delayed messages from the same sender in the same time slot, a situation that can happen in practice. Both models admit a description of the consensus updates in the presence of delays via linear equations. Finally, we briefly discuss how to apply our delay models to analyze distributed optimization algorithms in the presence of delayed information. I.
Consensusbased distributed optimization: Practical issues and applications in largescale machine learning
 in Allerton Conference
, 2012
"... Abstract — This paper discusses practical consensusbased distributed optimization algorithms. In consensusbased optimization algorithms, nodes interleave local gradient descent steps with consensus iterations. Gradient steps drive the solution to a minimizer, while the consensus iterations synchr ..."
Abstract

Cited by 11 (3 self)
 Add to MetaCart
(Show Context)
Abstract — This paper discusses practical consensusbased distributed optimization algorithms. In consensusbased optimization algorithms, nodes interleave local gradient descent steps with consensus iterations. Gradient steps drive the solution to a minimizer, while the consensus iterations synchronize the values so that all nodes converge to a networkwide optimum when the objective is convex and separable. The consensus update requires communication. If communication is synchronous and nodes wait to receive one message from each of their neighbors before updating then progress is limited by the slowest node. To be robust to failing or stalling nodes, asynchronous communications should be used. Asynchronous protocols using bidirectional communications cause deadlock, and so onedirectional protocols are necessary. However, with onedirectional asynchronous protocols it is no longer possible to guarantee the consensus matrix is doubly stochastic. At the same time it is essential that the coordination protocol achieve consensus on the average to avoid biasing the optimization objective. We report on experiments running PushSum Distributed Dual Averaging for convex optimization in a MPI cluster. The experiments illustrate the benefits of using asynchronous consensusbased distributed optimization when some nodes are unreliable and may fail or when messages experience timevarying delays. I.
Convergence results for the linear consensus problem under Markovian random graphs
, 2009
"... Abstract. This paper discusses the linear asymptotic consensus problem for a network of dynamic agents whose communication network is modeled by a randomly switching graph. The switching is determined by a finite state Markov process, each topology corresponding to a state of the process. We address ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
(Show Context)
Abstract. This paper discusses the linear asymptotic consensus problem for a network of dynamic agents whose communication network is modeled by a randomly switching graph. The switching is determined by a finite state Markov process, each topology corresponding to a state of the process. We address the cases where the dynamics of the agents is expressed both in continuous time and in discrete time. We show that, if the consensus matrices are doubly stochastic, average consensus is achieved in the mean square sense and the almost sure sense if and only if the graph resulting from the union of graphs corresponding to the states of the Markov process is strongly connected. The aim of this paper is to show how techniques from the theory of Markovian jump linear systems, in conjunction with results inspired by matrix and graph theory, can be used to prove convergence results for stochastic consensus problems.
Consensus and products of random stochastic matrices: Exact rate for convergence in probability
 Carnegie Mellon University (CMU
, 2013
"... Abstract—We find the exact rate for convergence in probability of products of independent, identically distributed symmetric, stochastic matrices. It is wellknown that if the matrices have positive diagonals almost surely and the support graph of the mean or expected value of the random matrices ..."
Abstract

Cited by 8 (6 self)
 Add to MetaCart
(Show Context)
Abstract—We find the exact rate for convergence in probability of products of independent, identically distributed symmetric, stochastic matrices. It is wellknown that if the matrices have positive diagonals almost surely and the support graph of the mean or expected value of the random matrices is connected, the products of the matrices converge almost surely to the average consensus matrix, and thus in probability. In this paper, we show that the convergence in probability is exponentially fast, and we explicitly characterize the exponential rate of this convergence. Our analysis reveals that the exponential rate of convergence in probability depends only on the statistics of the support graphs of the randommatrices. Further, we show how to compute this rate for commonly used randommodels: gossip and link failure.With thesemodels, the rate is found by solving a mincut problem, and hence it is easily computable. Finally, as an illustration, we apply our results to solving power allocation among networked sensors in a consensus+innovations distributed detection problem. Index Terms—Consensus, consensus innovations, convergence in probability, exponential rate, performance analysis, random network. I.
Distributed algorithms for consensus and coordination in the presence of packetdropping communication links  part ii: Coefficients of ergodicity analysis approach
 CoRR
, 2011
"... ar ..."
1 An asynchronous consensusbased algorithm for estimation from noisy relative measurements
"... Abstract—In this work we address the problem of optimal estimating the position of each agent in a network from relative noisy vectorial distances with its neighbors. Although the problem can be cast as a standard leastsquares problem, the main challenge is to devise scalable algorithms that allow ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
Abstract—In this work we address the problem of optimal estimating the position of each agent in a network from relative noisy vectorial distances with its neighbors. Although the problem can be cast as a standard leastsquares problem, the main challenge is to devise scalable algorithms that allow each agent to estimate its own position by means of only local communication and bounded complexity, independently of the network size and topology. We propose a consensusbased algorithm with the use of local memory variables which allows asynchronous implementation, has guaranteed exponential convergence to the optimal solution under mild deterministic and randomised communication protocols, and requires minimal packet transmission. In the randomized scenario we then study the rate of convergence in expectation of the estimation error and we argue that it can be used to obtain upper and lower bound for the rate of converge in mean square. In particular, we show that for regular graphs the convergence rate in expectation is reduced by a factor N, which is the number of nodes, which is the same asymptotic degradation of memoryless asynchronous consensus algorithms. Additionally, we show that the asynchronous implementation is also robust to delays and communication failures. We finally complement the analytical results with some numerical simulations comparing the proposed strategy with other algorithms which have been recently proposed in the literature. Index Terms—Wireless sensor networks, distributed localization algorithms, consensus algorithms I.
Information spread in networks: Control, games, and equilibria
"... Abstract—We design intervention schemes to control information spread in multiagent systems. We consider two information spread models: linear distributed averaging and virus spread dynamics. Using the framework of differential games, we design a dynamical optimization framework that produces stra ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract—We design intervention schemes to control information spread in multiagent systems. We consider two information spread models: linear distributed averaging and virus spread dynamics. Using the framework of differential games, we design a dynamical optimization framework that produces strategies that are robust to adversarial intervention. For linear dynamics, we show that optimal strategies make connection to potentialtheory. In the virus spread case, we show that optimal controllers exhibit multiple switches. Moreover, we establish a connection between game theory and dynamical descriptions of network epidemics, which provides insights into decision making in infected networks. Finally, we present initial building blocks for network controllability using a limited number of controls. I.