  Recently, research on accelerated stochastic gradient descent methods (e.g.,
SVRG) has made exciting progress (e.g., linear convergence for strongly convex
problems). However, the best-known methods (e.g., Katyusha) requires at least
two auxiliary variables and two momentum parameters. In this paper, we propose
a fast stochastic variance reduction gradient (FSVRG) method, in which we
design a novel update rule with the Nesterov's momentum and incorporate the
technique of growing epoch size. FSVRG has only one auxiliary variable and one
momentum weight, and thus it is much simpler and has much lower per-iteration
complexity. We prove that FSVRG achieves linear convergence for strongly convex
problems and the optimal $\mathcal{O}(1/T^2)$ convergence rate for non-strongly
convex problems, where $T$ is the number of outer-iterations. We also extend
FSVRG to directly solve the problems with non-smooth component functions, such
as SVM. Finally, we empirically study the performance of FSVRG for solving
various machine learning problems such as logistic regression, ridge
regression, Lasso and SVM. Our results show that FSVRG outperforms the
state-of-the-art stochastic methods, including Katyusha.
