ICML 2018oral25 citations
Katyusha X: Simple Momentum Method for Stochastic Sum-of-Nonconvex Optimization
Abstract
The problem of minimizing sum-of-nonconvex functions (i.e., convex functions that are average of non-convex ones) is becoming increasing important in machine learning, and is the core machinery for PCA, SVD, regularized Newton’s method, accelerated non-convex optimization, and more. We show how to provably obtain an accelerated stochastic algorithm for minimizing sum-of-nonconvex functions, by adding one additional line to the well-known SVRG method. This line corresponds to momentum, and shows how to directly apply momentum to the finite-sum stochastic minimization of sum-of-nonconvex functions. As a side result, our method enjoys linear parallel speed-up using mini-batch.
BibTeX
@InProceedings{pmlr-v80-allen-zhu18a,
title = {{K}atyusha X: Simple Momentum Method for Stochastic Sum-of-Nonconvex Optimization},
author = {Allen-Zhu, Zeyuan},
booktitle = {Proceedings of the 35th International Conference on Machine Learning},
pages = {179--185},
year = {2018},
editor = {Dy, Jennifer and Krause, Andreas},
volume = {80},
series = {Proceedings of Machine Learning Research},
month = {10--15 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v80/allen-zhu18a/allen-zhu18a.pdf},
url = {https://proceedings.mlr.press/v80/allen-zhu18a.html},
abstract = {The problem of minimizing sum-of-nonconvex functions (i.e., convex functions that are average of non-convex ones) is becoming increasing important in machine learning, and is the core machinery for PCA, SVD, regularized Newton’s method, accelerated non-convex optimization, and more. We show how to provably obtain an accelerated stochastic algorithm for minimizing sum-of-nonconvex functions, by adding one additional line to the well-known SVRG method. This line corresponds to momentum, and shows how to directly apply momentum to the finite-sum stochastic minimization of sum-of-nonconvex functions. As a side result, our method enjoys linear parallel speed-up using mini-batch.}
}