A randomized gossip consensus algorithm on convex metric spaces
A randomized gossip consensus algorithm on convex metric spaces
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Date
2012-02-20
Authors
Matei, Ion
Somarakis, Christoforos
Baras, John
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Abstract
A consensus problem consists of a group of dynamic agents who seek to agree upon certain quantities of
interest. This problem can be generalized in the context of convex metric spaces that extend the standard notion
of convexity. In this paper we introduce and analyze a randomized gossip algorithm for solving the generalized
consensus problem on convex metric spaces. We study the convergence properties of the algorithm using stochastic
differential equations theory. We show that the dynamics of the distances between the states of the agents can be
upper bounded by the dynamics of a stochastic differential equation driven by Poisson counters. In addition, we
introduce instances of the generalized consensus algorithm for several examples of convex metric spaces together
with numerical simulations.