Randomized coordinate gradient descent almost surely escapes strict saddle points
Optimization and Control
2025-08-12 v1 Numerical Analysis
Dynamical Systems
Numerical Analysis
Probability
Abstract
We analyze the behavior of randomized coordinate gradient descent for nonconvex optimization, proving that under standard assumptions, the iterates almost surely escape strict saddle points. By formulating the method as a nonlinear random dynamical system and characterizing neighborhoods of critical points, we establish this result through the center-stable manifold theorem.
Cite
@article{arxiv.2508.07535,
title = {Randomized coordinate gradient descent almost surely escapes strict saddle points},
author = {Ziang Chen and Yingzhou Li and Zihao Li},
journal= {arXiv preprint arXiv:2508.07535},
year = {2025}
}