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
Text
Moritz et al. "A Linearly-Convergent Stochastic L-BFGS Algorithm." International Conference on Artificial Intelligence and Statistics, 2016.Markdown
[Moritz et al. "A Linearly-Convergent Stochastic L-BFGS Algorithm." International Conference on Artificial Intelligence and Statistics, 2016.](https://mlanthology.org/aistats/2016/moritz2016aistats-linearly/)BibTeX
@inproceedings{moritz2016aistats-linearly,
title = {{A Linearly-Convergent Stochastic L-BFGS Algorithm}},
author = {Moritz, Philipp and Nishihara, Robert and Jordan, Michael I.},
booktitle = {International Conference on Artificial Intelligence and Statistics},
year = {2016},
pages = {249-258},
url = {https://mlanthology.org/aistats/2016/moritz2016aistats-linearly/}
}