Multi-agent mirror descent for decentralized stochastic optimization

We develop a decentralized algorithm for stochastic composite optimization problems, combining ideas from consensus-based multi-agent optimization and the celebrated mirror descent algorithm. When the composite regularization term is strongly convex, the proposed method is shown to converge at a rate of O(1/k) where k is the number of iterations executed. This is known to be the best possible rate of convergence for the class of problems considered. Moreover, theory and experiments show that the speedup of the proposed methods-the number of iterations required to reach a desired level of accuracy-scales linearly with the number of nodes in the network.