Proximal methods avoid active strict saddles of weakly convex functions
Optimization and Control
2021-02-18 v2 Machine Learning
Machine Learning
Abstract
We introduce a geometrically transparent strict saddle property for nonsmooth functions. This property guarantees that simple proximal algorithms on weakly convex problems converge only to local minimizers, when randomly initialized. We argue that the strict saddle property may be a realistic assumption in applications, since it provably holds for generic semi-algebraic optimization problems.
Cite
@article{arxiv.1912.07146,
title = {Proximal methods avoid active strict saddles of weakly convex functions},
author = {Damek Davis and Dmitriy Drusvyatskiy},
journal= {arXiv preprint arXiv:1912.07146},
year = {2021}
}
Comments
43 pages, 2 figures