Consensus in the Wasserstein Metric Space of Probability Measures

摘要

Distributed consensus in the Wasserstein metric space of probability measuresis introduced in this work. Convergence of each agent's measure to a commonmeasure value is proven under a weak network connectivity condition. The commonmeasure reached at each agent is one minimizing a weighted sum of itsWasserstein distance to all initial agent measures. This measure is known asthe Wasserstein barycentre. Special cases involving Gaussian measures,empirical measures, and time-invariant network topologies are considered, whereconvergence rates and average-consensus results are given. This algorithm haspotential applicability in computer vision, machine learning and distributedestimation, etc.