On Convergence of Incremental Gradient for Non-convex Smooth Functions
Anastasia Koloskova, Nikita Doikov, Sebastian U Stich, Martin Jaggi
Abstract
In machine learning and neural network optimization, algorithms like incremental gradient, single shuffle SGD, and random reshuffle SGD are popular due to their cache-mismatch efficiency and good practical convergence behavior. However, their optimization properties in theory, especially for non-convex smooth functions, remain incompletely explored. This paper delves into the convergence properties of SGD algorithms with arbitrary data ordering, within a broad framework for non-convex smooth functions. Our findings show enhanced convergence guarantees for incremental gradient and single shuffle SGD. Particularly if $n$ is the training set size, we improve $n$ times the optimization term of convergence guarantee to reach accuracy $\epsilon$ from $O \left( \frac{n}{\epsilon} \right)$ to $O \left( \frac{1}{\epsilon}\right)$.
BibTeX
@inproceedings{
koloskova2024on,
title={On Convergence of Incremental Gradient for Non-convex Smooth Functions},
author={Anastasia Koloskova and Nikita Doikov and Sebastian U Stich and Martin Jaggi},
booktitle={Forty-first International Conference on Machine Learning},
year={2024},
url={https://openreview.net/forum?id=ZRMQX6aTUS}
}