Modified Stochastic Extragradient Methods for Stochastic Variational Inequality (Journal of Computational Mathematics, 2024)
In this paper, we consider two kinds of extragradient methods to solve the pseudo-monotone stochastic variational inequality problem. First, we present the modified stochastic extragradient method with constant step-size (MSEGMC) and prove the convergenceof it. With the strong pseudo-monotone operator and the exponentially growing samplesequences, we establish the $R$-linear convergence rate in terms of the mean natural residualand the oracle complexity $O(1/\epsilon).$ Second, we propose a modified stochastic extragradientmethod with adaptive step-size (MSEGMA). In addition, the step-size of MSEGMA doesnot depend on the Lipschitz constant and without any line-search procedure. Finally, weuse some numerical experiments to verify the effectiveness of the two algorithms.