Accelerated Stochastic Algorithms for Convex-Concave Saddle-Point Problems

We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in primal variable, we first restart scheme for this problem. gradient noises obey sub-Gaussian distributions, oracle complexity our strictly better than any existing methods, even deterministic case. Furthermore, each problem parameter interest, whenever lower bound exists, either optimal or nearly (up log factor). The subroutine used itself new algorithm developed where nonstrongly variable. This algorithm, which based on hybrid framework, achieves state-of-the-art and may be independent interest.