Second-order Properties of Noisy Distributed Gradient Descent
Optimization and Control
2023-07-21 v2
Abstract
We study a fixed step-size noisy distributed gradient descent algorithm for solving optimization problems in which the objective is a finite sum of smooth but possibly non-convex functions. Random perturbations are introduced to the gradient descent directions at each step to actively evade saddle points. Under certain regularity conditions, and with a suitable step-size, it is established that each agent converges to a neighborhood of a local minimizer and the size of the neighborhood depends on the step-size and the confidence parameter. A numerical example is presented to illustrate the effectiveness of the random perturbations in terms of escaping saddle points in fewer iterations than without the perturbations.
Cite
@article{arxiv.2303.17165,
title = {Second-order Properties of Noisy Distributed Gradient Descent},
author = {Lei Qin and Michael Cantoni and Ye Pu},
journal= {arXiv preprint arXiv:2303.17165},
year = {2023}
}