A fast stochastic approximation-based subgradient extragradient algorithm with variance reduction for solving stochastic variational inequality problems

Abstract

In this paper, we propose a fast stochastic approximation-based subgradient extragradient algorithm with variance reduction for solving the stochastic variational inequality, where the Lipschitz constant is not necessarily known. Each iteration of our algorithm requires only one projection and one oracle call, and so reducing the computation time. By combining the iterative variance reduction procedure and the stochastic approximation approach, we discuss the asymptotic convergence, the optimal oracle complexity and the sublinear convergence rate in terms of the mean natural residual function. We also obtain the linear convergence rate with finite computational budget under the assumption of the strongly Minty variational inequality and the bounded projection error bound condition, respectively. Finally, several numerical experiments illustrate the efficiency and competitiveness of the proposed algorithm.