The geometry of a probabilistic consensus of opinion algorithm

Ion Matei, John S. Baras
2011 Proceedings of the 2011 American Control Conference  
We consider the problem of a group of agents whose objective is to asymptotically reach agreement of opinion. The agents exchange information subject to a communication topology modeled by a time varying graph. The agents use a probabilistic algorithm under which at each time instant an agent updates its state by probabilistically choosing from its current state/opinion and the ones of its neighbors. We show that under some minimal assumptions on the communication topology (infinitely often
more » ... ectivity and bounded intercommunication time between agents), the agents reach agreement with probability one. We show that this algorithm has the same geometric properties as the linear consensus algorithm in R n . More specifically, we show that the probabilistic update scheme of an agent is equivalent to choosing a point from the (generalized) convex hull of its current state and the states of its neighbors; convex hull defined on a particular convex metric space where the states of the agents live and for which a detailed description is given. CONFIDENTIAL. Limited circulation. For review only.
doi:10.1109/acc.2011.5991448 fatcat:2yzmdmysrnbohdbggqaiq74vre