  We study the decentralized distributed computation of discrete approximations
for the regularized Wasserstein barycenter of a finite set of continuous
probability measures distributedly stored over a network. We assume there is a
network of agents/machines/computers, and each agent holds a private continuous
probability measure and seeks to compute the barycenter of all the measures in
the network by getting samples from its local measure and exchanging
information with its neighbors. Motivated by this problem, we develop, and
analyze, a novel accelerated primal-dual stochastic gradient method for general
stochastic convex optimization problems with linear equality constraints. Then,
we apply this method to the decentralized distributed optimization setting to
obtain a new algorithm for the distributed semi-discrete regularized
Wasserstein barycenter problem. Moreover, we show explicit non-asymptotic
complexity for the proposed algorithm.

Optimization and Control;Distributed, Parallel, and Cluster Computing