k-SVRG: Variance Reduction for Large Scale Optimization

Abstract: Variance reduced stochastic gradient (SGD) methods converge significantly faster than the vanilla SGD counterpart. However, these methods are not very practical on large scale problems, as they either i) require frequent passes over the full data to recompute gradients---without making any progress during this time (like for SVRG), or ii)~they require additional memory that can surpass the size of the input problem (like for SAGA). In this work, we propose $k$-SVRG that addresses these issues by making best use of the \emph{available} memory and minimizes the stalling phases without progress. We prove linear convergence of $k$-SVRG on strongly convex problems and convergence to stationary points on non-convex problems. Numerical experiments show the effectiveness of our method.