Escaping Saddle Points with Adaptive Gradient Methods
Name
staib19a.pdf
Description
Published version
Size
621.37 KB
Format
Adobe PDF
Checksum (MD5)
2b4bac7e2711abd8c1e9f31df9167127
Author(s)
Staib, Matthew
Reddi, Sashank
Kale, Satyen
Kumar, Sanjiv
Sra, Suvrit
Date Issued
2019
Journal
36th International Conference on Machine Learning, ICML 2019
Citation
Staib, Matthew, Reddi, Sashank, Kale, Satyen, Kumar, Sanjiv and Sra, Suvrit. 2019. "Escaping Saddle Points with Adaptive Gradient Methods." 36th International Conference on Machine Learning, ICML 2019, 2019-June.
Version
Final published version
Abstract
© 2019 International Machine Learning Society (IMLS). Adaptive methods such as Adam and RMSProp are widely used in deep learning but are not well understood. In this paper, we seek a crisp, clean and precise characterization of their behavior in nonconvex settings. To this end, we first provide a novel view of adaptive methods as preconditioned SGD, where the preconditioner is estimated in an online manner. By studying the preconditioner on its own, we elucidate its purpose: it rescales the stochastic gradient noise to be isotropic near stationary points, which helps escape saddle points. Furthermore, we show that adaptive methods can efficiently estimate the aforementioned preconditioner. By gluing together these two components, we provide the first (to our knowledge) second-order convergence result for any adaptive method. The key insight from our analysis is that, compared to SGD, adaptive methods escape saddle points faster, and can converge faster overall to second-order stationary points.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
http://proceedings.mlr.press/v97/staib19a.html
