Reaching Consensus with Imprecise Probabilities Over a Network

Abstract

Information consensus in sensor networks has received much attention due to its numerous applications in distributed decision making. This paper discusses the problem of a distributed group of agents coming to agreement on a probability vector over a network, such as would be required in a decentralized estimation of state transition probabilities or agreement on a probabilistic search map. Unique from other recent consensus literature, however, the agents in this problem must reach agreement while accounting for the uncertainties in their respective probabilities, which are formulated according to generally non-Gaussian distributions. The first part of this paper considers the problem in which the agents seek agreement to the centralized Bayesian estimate of the probabilities, which is accomplished using consensus on hyperparameters. The second part shows that the new hyperparameter consensus methodology can ensure convergence to the centralized estimate even while measurements of a static process are occurring concurrently with the consensus algorithm. A machine repair example is used to illustrate the advantages of hyperparameter consensus over conventional consensus approaches.