Stochastic Bregman Extragradient Methods For Stochastic Variational Inequalities

We consider the convergence of stochastic Bregman extragradient methods for solving s-tochastic variational inequalities.We present a stochastic Bregman extragradient method and a mini-batch stochastic Bregman extragradient method.Assume that the operator is monotone and Lipschitz continuous,we show that the convergence rate of the stochastic Bregman extra-gradient method is(?).Then,as an application,we present the convergence results of the proposed method for solving stochastic saddle point problem.If the operator is monotone and H¨older continuous,we present the convergence results of the mini-batch stochastic Bregman extragradient method.Finally,we point out that the standard variance uniformly bounded assumption is not required in our analysis.