Stochastic Recursive Gradient Algorithm for Nonconvex Optimization

TL;DR

This paper introduces a mini-batch stochastic recursive gradient algorithm called SARAH for nonconvex optimization, demonstrating improved convergence rates for general and gradient dominated functions.

Contribution

It provides the first analysis of SARAH's convergence rates for nonconvex loss minimization, including sublinear and linear rates under different conditions.

Findings

Sublinear convergence rate to stationary points for general nonconvex functions.

Linear convergence rate for gradient dominated functions.

Advantages over other stochastic gradient algorithms.

Abstract

In this paper, we study and analyze the mini-batch version of StochAstic Recursive grAdient algoritHm (SARAH), a method employing the stochastic recursive gradient, for solving empirical loss minimization for the case of nonconvex losses. We provide a sublinear convergence rate (to stationary points) for general nonconvex functions and a linear convergence rate for gradient dominated functions, both of which have some advantages compared to other modern stochastic gradient algorithms for nonconvex losses.