MaSS: an Accelerated Stochastic Method for Over-parametrized Learning

In this paper we introduce MaSS (Momentum-added Stochastic Solver), an accelerated SGD method for optimizing over-parameterized networks. Our method is simple and efficient to implement and does not require changing parameters or computing full gradients in the course of optimization. We provide a detailed theoretical analysis for convergence and parameter selection including their dependence on the mini-batch size in the quadratic case. We also provide theoretical convergence results for a more general convex setting. We provide an experimental evaluation showing strong performance of our method in comparison to Adam and SGD for several standard architectures of deep networks including ResNet, convolutional and fully connected networks. We also show its performance for convex kernel machines.