A Generic Approach for Escaping Saddle points
Abstract
A central challenge to using first-order methods for optimizing nonconvex problems is the presence of saddle points. First-order methods often get stuck at saddle points, greatly deteriorating their performance. Typically, to escape from saddles one has to use second-order methods. However, most works on second-order methods rely extensively on expensive Hessian-based computations, making them impractical in large-scale settings. To tackle this challenge, we introduce a generic framework that minimizes Hessian based computations while at the same time provably converging to second-order critical points. Our framework carefully alternates between a first-order and a second-order subroutine, using the latter only close to saddle points, and yields convergence results competitive to the state-of-the-art. Empirical results suggest that our strategy also enjoys a good practical performance.
Cite
@article{arxiv.1709.01434,
title = {A Generic Approach for Escaping Saddle points},
author = {Sashank J Reddi and Manzil Zaheer and Suvrit Sra and Barnabas Poczos and Francis Bach and Ruslan Salakhutdinov and Alexander J Smola},
journal= {arXiv preprint arXiv:1709.01434},
year = {2017}
}