Distributed Optimization with Quantization for Computing Wasserstein Barycenters

Roman Krawtschenko, César A. Uribe, Alexander V. Gasnikov, Pavel E. Dvurechensky

Abstract: We study the problem of the decentralized computation of (entropy-regularized) semi-discrete fixed-support 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 in a distributed manner. The iteration, sample, computational, and communication complexities of the proposed algorithm are shown, including dependency on the support size, the number of distributions, the desired accuracy, and the characteristics of the network. Numerical results validate our algorithmic analysis.

External IDs:dblp:conf/cdc/KrawtschenkoUGD25