  Stochastic variance-reduced gradient (SVRG) is a classical optimization
method. Although it is theoretically proved to have better convergence
performance than stochastic gradient descent (SGD), the generalization
performance of SVRG remains open. In this paper we investigate the effects of
some training techniques, mini-batching and learning rate decay, on the
generalization performance of SVRG, and verify the generalization performance
of Batch-SVRG (B-SVRG). In terms of the relationship between optimization and
generalization, we believe that the average norm of gradients on each training
sample as well as the norm of average gradient indicate how flat the landscape
is and how well the model generalizes. Based on empirical observations of such
metrics, we perform a sign switch on B-SVRG and derive a practical algorithm,
BatchPlus-SVRG (BP-SVRG), which is numerically shown to enjoy better
generalization performance than B-SVRG, even SGD in some scenarios of deep
neural networks.
