Distributed Optimization with Quantization for Computing Wasserstein Barycenters

TL;DR

This paper introduces a decentralized algorithm for computing entropy-regularized Wasserstein barycenters using quantized sampling gradients, enabling efficient distributed computation over networks.

Contribution

It proposes a novel sampling gradient quantization scheme for decentralized Wasserstein barycenter computation, with explicit complexity analysis and validation.

Findings

Efficient communication via gradient quantization

Explicit complexity bounds depending on network size and accuracy

Numerical validation of the proposed method

Abstract

We study the problem of the decentralized computation of entropy-regularized semi-discrete Wasserstein barycenters over a network. Building upon recent primal-dual approaches, we propose a sampling gradient quantization scheme that allows efficient communication and computation of approximate barycenters where the factor distributions are stored distributedly on arbitrary networks. The communication and algorithmic complexity of the proposed algorithm are shown, with explicit dependency on the size of the support, the number of distributions, and the desired accuracy. Numerical results validate our algorithmic analysis.