Degenerate Stochastic Delay Modified Equation: Approximation of Stochastic Variance Reduced Gradient

Abstract

According to the property of stochastic variance reduced gradient (SVRG) algorithms, we construct a class of degenerate stochastic delay modified equations (SDMEs). Using the Lindeberg principle and the Markov property, we approximate the SVRG algorithms by the corresponding SDMEs. We obtain order 1 weak approximation in the smooth Wasserstein distance and the theory is validated through numerical experiments.