Federated Calculation of the Free-Support Transportation Barycenter by Single-Loop Dual Decomposition
This work addresses the challenge of distributed data privacy and computational efficiency for machine learning practitioners, though it appears incremental as it builds on existing dual decomposition methods.
The authors tackled the problem of efficiently computing the Wasserstein barycenter with free support in a federated setting, achieving low iteration complexity and scalability without accessing local data or solving repeated transportation problems.
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.