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.

Cite

Text

Allen-Zhu. "Katyusha X: Simple Momentum Method for Stochastic Sum-of-Nonconvex Optimization." International Conference on Machine Learning, 2018.

Markdown

[Allen-Zhu. "Katyusha X: Simple Momentum Method for Stochastic Sum-of-Nonconvex Optimization." International Conference on Machine Learning, 2018.](https://mlanthology.org/icml/2018/allenzhu2018icml-katyusha/)

BibTeX

@inproceedings{allenzhu2018icml-katyusha,
  title     = {{Katyusha X: Simple Momentum Method for Stochastic Sum-of-Nonconvex Optimization}},
  author    = {Allen-Zhu, Zeyuan},
  booktitle = {International Conference on Machine Learning},
  year      = {2018},
  pages     = {179-185},
  volume    = {80},
  url       = {https://mlanthology.org/icml/2018/allenzhu2018icml-katyusha/}
}