A Linearly-Convergent Stochastic L-BFGS Algorithm

TL;DR

This paper introduces a stochastic L-BFGS algorithm with proven linear convergence for strongly convex functions, combining variance reduction techniques and demonstrating strong empirical performance on large-scale problems.

Contribution

It presents a novel stochastic L-BFGS algorithm with a proven linear convergence rate, integrating variance reduction methods for improved optimization efficiency.

Findings

Algorithm exhibits linear convergence on convex problems.

Performs well on large-scale convex and non-convex problems.

Effective across a wide range of step sizes.

Abstract

We propose a new stochastic L-BFGS algorithm and prove a linear convergence rate for strongly convex and smooth functions. Our algorithm draws heavily from a recent stochastic variant of L-BFGS proposed in Byrd et al. (2014) as well as a recent approach to variance reduction for stochastic gradient descent from Johnson and Zhang (2013). We demonstrate experimentally that our algorithm performs well on large-scale convex and non-convex optimization problems, exhibiting linear convergence and rapidly solving the optimization problems to high levels of precision. Furthermore, we show that our algorithm performs well for a wide-range of step sizes, often differing by several orders of magnitude.