Federated Calculation of the Free-Support Transportation Barycenter by Single-Loop Dual Decomposition

TL;DR

This paper introduces a scalable federated dual decomposition algorithm for computing Wasserstein barycenters without accessing local data or solving multiple transportation problems, demonstrating efficiency and scalability.

Contribution

It presents a novel federated dual decomposition method that reduces computational complexity and enhances scalability for Wasserstein barycenter calculation.

Findings

Algorithm exhibits low per-iteration complexity

It does not require local data access or repeated transportation problem solutions

Outperforms state-of-the-art methods on mixture model examples

Abstract

We propose an efficient federated dual decomposition algorithm for calculating the Wasserstein barycenter of several distributions, including choosing the support of the solution. The algorithm does not access local data and uses only highly aggregated information. It also does not require repeated solutions to mass transportation problems. Because of the absence of any matrix-vector operations, the algorithm exhibits a very low complexity of each iteration and significant scalability. We illustrate its virtues and compare it to the state-of-the-art methods on several examples of mixture models.