A stochastic primal-dual algorithm for composite constrained optimization

This paper studies the decentralized stochastic optimization problem over an undirected network, where each agent owns its local private functions made up of two non-smooth functions and an expectation-valued function. A decentralized stochastic primal-dual algorithm is proposed, by combining the variance-reduced method and the stochastic approximation method. The local gradients are estimated by using the mean of a variable number of sample gradients and the stochastic error decreases with the number of samples in the stochastic approximation process. The highlight of this paper is the extension of the primal-dual algorithm to the stochastic optimization problems. The effectiveness of the proposed algorithm and the correctness of the theory are verified by numerical experiments.