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533
Distributed consensus algorithms in sensor networks with communication channel noise and random link failures
- in Proc. 41st Asilomar Conf. Signals, Systems, Computers
, 2007
"... Abstract—The paper studies average consensus with random topologies (intermittent links) and noisy channels. Consensus with noise in the network links leads to the bias-variance dilemma—running consensus for long reduces the bias of the final average estimate but increases its variance. We present t ..."
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Cited by 149 (21 self)
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Abstract—The paper studies average consensus with random topologies (intermittent links) and noisy channels. Consensus with noise in the network links leads to the bias-variance dilemma—running consensus for long reduces the bias of the final average estimate but increases its variance. We present two different compromises to this tradeoff: the algorithm modifies conventional consensus by forcing the weights to satisfy a persistence condition (slowly decaying to zero;) and the algorithm where the weights are constant but consensus is run for a fixed number of iterations, then it is restarted and rerun for a total of runs, and at the end averages the final states of the runs (Monte Carlo averaging). We use controlled Markov processes and stochastic approximation arguments to prove almost sure convergence of to a finite consensus limit and compute explicitly the mean square error (mse) (variance) of the consensus limit. We show that represents the best of both worlds—zero bias and low variance—at the cost of a slow convergence rate; rescaling the weights balances the variance versus the rate of bias reduction (convergence rate). In contrast, , because of its constant weights, converges fast but presents a different bias-variance tradeoff. For the same number of iterations, shorter runs (smaller) lead to high bias but smaller variance (larger number of runs to average over.) For a static nonrandom network with Gaussian noise, we compute the optimal gain for to reach in the shortest number of iterations, with high probability (1), ()-consensus ( residual bias). Our results hold under fairly general assumptions on the random link failures and communication noise. Index Terms—Additive noise, consensus, sensor networks, stochastic approximation, random topology. I.
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 133 (3 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 worst-case convergence time for various classes of linear, time-invariant, distributed consensus methods, and provide an algorithm that essentially matches those lower bounds. We then consider the case of a time-varying topology, and provide a polynomial-time averaging algorithm.
Gossip algorithms for distributed signal processing
- PROCEEDINGS OF THE IEEE
, 2010
"... Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the co ..."
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Cited by 116 (30 self)
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Gossip algorithms are attractive for in-network processing in sensor networks because they do not require any specialized routing, there is no bottleneck or single point of failure, and they are robust to unreliable wireless network conditions. Recently, there has been a surge of activity in the computer science, control, signal processing, and information theory communities, developing faster and more robust gossip algorithms and deriving theoretical performance guarantees. This paper presents an overview of recent work in the area. We describe convergence rate results, which are related to the number of transmittedmessages and thus the amount of energy consumed in the network for gossiping. We discuss issues related to gossiping over wireless links, including the effects of quantization and noise, and we illustrate the use of gossip algorithms for canonical signal processing tasks including distributed estimation, source localization, and compression.
Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling
- IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2010
"... The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multiagen ..."
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Cited by 97 (12 self)
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The goal of decentralized optimization over a network is to optimize a global objective formed by a sum of local (possibly nonsmooth) convex functions using only local computation and communication. It arises in various application domains, including distributed tracking and localization, multiagent co-ordination, estimation in sensor networks, and largescale machine learning. We develop and analyze distributed algorithms based on dual subgradient averaging, and we provide sharp bounds on their convergence rates as a function of the network size and topology. Our analysis allows us to clearly separate the convergence of the optimization algorithm itself and the effects of communication dependent on the network structure. We show that the number of iterations required by our algorithm scales inversely in the spectral gap of the network and confirm this prediction’s sharpness both by theoretical lower bounds and simulations for various networks. Our approach includes the cases of deterministic optimization and communication as well as problems with stochastic optimization and/or communication.
Broadcast gossip algorithms for consensus
- IEEE TRANS. SIGNAL PROCESS
, 2009
"... Motivated by applications to wireless sensor, peer-to-peer, 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 broadcasting-based gossiping algorithm to compute the (possib ..."
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Cited by 93 (7 self)
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Motivated by applications to wireless sensor, peer-to-peer, 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 broadcasting-based 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 broad-cast 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.
A necessary and sufficient condition for consensus over random networks
- IEEE Transactions on Automatic Control
, 2008
"... Abstract — In this paper we consider the consensus problem for stochastic switched linear dynamical systems. For discretetime and continuous-time stochastic switched linear systems, we present necessary and sufficient conditions under which such systems reach a consensus almost surely. In the discre ..."
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Cited by 89 (6 self)
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Abstract — In this paper we consider the consensus problem for stochastic switched linear dynamical systems. For discretetime and continuous-time stochastic switched linear systems, we present necessary and sufficient conditions under which such systems reach a consensus almost surely. In the discrete-time case, our assumption is that the underlying graph of the system at any given time instance is derived from a random graph process, independent of other time instances. These graphs can be weighted, directed and with dependent edges. For the continuous-time case, we assume that the switching is governed by a Poisson point process and the graphs characterizing the topology of the system are independent and identically distributed over time. For both such frameworks, we present necessary and sufficient conditions for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments. These easily verifiable conditions depend on the spectrum of the average weight matrix and the average Laplacian matrix for the discrete-time and continuous-time cases, respectively. I.
Communication Constraints in the Average Consensus Problem
, 2007
"... The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems, such as the coordination of a team of autonomous agents. In such a problem, communication constraints impose limits on the achievable control performance. We cons ..."
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Cited by 81 (19 self)
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The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems, such as the coordination of a team of autonomous agents. In such a problem, communication constraints impose limits on the achievable control performance. We consider as instance of coordination the consensus problem. The aim of the paper is to characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the consensus. We show that time-invariant communication networks with circulant symmetries yield slow convergence if the amount of information exchanged by the agents does not scale well with their number. On the other hand, we show that randomly time-varying communication networks allow very fast convergence rates. We also show that, by adding logarithmic quantized data links to time-invariant networks with symmetries, control performance significantly improves with little growth of the required communication effort.
Optimal and scalable distribution of content updates over a mobile social network
- In Proc. IEEE INFOCOM
, 2009
"... Number: CR-PRL-2008-08-0001 ..."
Geographic gossip: Efficient averaging for sensor networks
- IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 2008
"... Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste of energy by repeatedly recirculating redundant information. For re ..."
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Cited by 65 (8 self)
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Gossip algorithms for distributed computation are attractive due to their simplicity, distributed nature, and robustness in noisy and uncertain environments. However, using standard gossip algorithms can lead to a significant waste of energy by repeatedly recirculating redundant information. For realistic sensor network model topologies like grids and random geometric graphs, the inefficiency of gossip schemes is related to the slow mixing times of random walks on the communication graph. We propose and analyze an alternative gossiping scheme that exploits geographic information. By utilizing geographic routing combined with a simple resampling method, we demonstrate substantial gains over previously proposed gossip protocols. For regular graphs such as the ring or grid, our algorithm improves standard gossip by factors of and, respectively. For the more challenging case of random geometric graphs, our algorithm computes the true average to accuracy using 1 5 1 ( ( log) log) radio transmissions, which yields a log factor improvement over standard gossip algorithms. We illustrate these theoretical results with experimental comparisons between our algorithm and standard methods as applied to various classes of random fields.
