Consensus in the Wasserstein Metric Space of Probability Measures
University of Technology Sydney Australia
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Distributed consensus in the Wasserstein metric space of probability measures is introduced in this work. Convergence of each agents measure to a common measure value is proven under a weak network connectivity condition. The common measure reached a teach agent is one minimizing a weighted sum of its Wasserstein distance to all initial agent measures. This measure is known as the Wasserstein bary centre. Special cases involving Gaussian measures, empirical measures, and time-invariant network topologies are considered, where convergence rates and average-consensus results are given. This algorithm has potential applicability in computer vision, machine learning and distributed estimation, etc.
- Operations Research
- Statistics and Probability