Distributed optimization with quantization for computing Wasserstein barycenters
- Krawchenko, Roman
- Uribe, César A.
- Gasnikov, Alexander
- Dvurechensky, Pavel
2010 Mathematics Subject Classification
- 90C25 90C30 90C06
- Distributed convex optimization, quantization, optimal transport, Wasserstein distance
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.