A Linearly-Convergent Stochastic L-BFGS Algorithm
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.
Cite
@article{arxiv.1508.02087,
title = {A Linearly-Convergent Stochastic L-BFGS Algorithm},
author = {Philipp Moritz and Robert Nishihara and Michael I. Jordan},
journal= {arXiv preprint arXiv:1508.02087},
year = {2016}
}
Comments
10 pages, 3 figures in International Conference on Artificial Intelligence and Statistics, 2016