ICML 2018oral25 citations

Katyusha X: Simple Momentum Method for Stochastic Sum-of-Nonconvex Optimization

Zeyuan Allen-Zhu

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.}
}