Federated Calculation of the Transportation Barycenter by a Dual Subgradient Method

We propose an efficient federated dual decomposition algorithm for calculating the free-support Wasserstein barycenter of several distributions. The algorithm does not have access to local data and uses only highly aggregated information. It avoids repeated solutions of mass transportation problems. Owing to the absence of any matrix-vector operations, the algorithm exhibits very low complexity of each iteration and significant scalability. We illustrate its virtues on mixture models.