Federated Calculation of the Transportation Barycenter by a Dual Subgradient Method

Zhengqi Lin, Andrzej Ruszczynski

Keywords: Wasserstein Barycenter, Subgradient Method, Federated Computing, Privacy

TL;DR: A dual decomposition algorithm calculates the Wasserstein barycenter of several distributions without access to local data and without repeated solutions of mass transportation problems.

Abstract: 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.

Submission Number: 6