2007/11/25 by Soummya Kar, José M. F. Moura, Kar, Soummya +1 · 8 citations
Computer Science · #Distributed Control Multi-Agent Systems #Distributed Sensor Networks and Detection Algorithms #Energy Efficient Wireless Sensor Networks #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Multiagent Systems (cs.MA) #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.0711.3915
openalex publication_date 2007/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 A-ND algorithm modifies conventional consensus by forcing the weights to satisfy a persistence condition (slowly decaying to zero); and the A-NC algorithm where the weights are constant but consensus is run for a fixed number of iterations \imath, then it is restarted and rerun for a total of p runs, and at the end averages the final states of the p runs (Monte Carlo averaging). We use controlled Markov processes and stochastic approximation arguments to prove almost sure convergence of A-ND to the desired average (asymptotic unbiasedness) and compute explicitly the m.s.e. (variance) of the consensus limit. We show that A-ND represents the best of both worlds--low bias and low variance--at the cost of a slow convergence rate; rescaling the weights...