Distributed Computation of Wasserstein Barycenters over Networks

TL;DR

This paper introduces a novel distributed algorithm enabling network nodes to collaboratively compute Wasserstein Barycenters through local interactions, with proven convergence and communication efficiency.

Contribution

It presents a class-optimal method for distributed Wasserstein Barycenter computation with convergence guarantees and communication complexity analysis.

Findings

Nodes can reach the barycenter through local interactions.

The method achieves arbitrary precision in finite communication rounds.

Communication complexity bounds are established for fixed undirected networks.

Abstract

We propose a new \cu{class-optimal} algorithm for the distributed computation of Wasserstein Barycenters over networks. Assuming that each node in a graph has a probability distribution, we prove that every node can reach the barycenter of all distributions held in the network by using local interactions compliant with the topology of the graph. We provide an estimate for the minimum number of communication rounds required for the proposed method to achieve arbitrary relative precision both in the optimality of the solution and the consensus among all agents for undirected fixed networks.