Gradient Descent Converges Linearly for Logistic Regression on Separable Data
Abstract
We show that running gradient descent with variable learning rate guarantees loss $f(x) ≤ 1.1 \cdot f(x^*)+\epsilon$ for the logistic regression objective, where the error $\epsilon$ decays exponentially with the number of iterations and polynomially with the magnitude of the entries of an arbitrary fixed solution $x$. This is in contrast to the common intuition that the absence of strong convexity precludes linear convergence of first-order methods, and highlights the importance of variable learning rates for gradient descent. We also apply our ideas to sparse logistic regression, where they lead to an exponential improvement of the sparsity-error tradeoff.
Cite
Text
Axiotis and Sviridenko. "Gradient Descent Converges Linearly for Logistic Regression on Separable Data." International Conference on Machine Learning, 2023.Markdown
[Axiotis and Sviridenko. "Gradient Descent Converges Linearly for Logistic Regression on Separable Data." International Conference on Machine Learning, 2023.](https://mlanthology.org/icml/2023/axiotis2023icml-gradient/)BibTeX
@inproceedings{axiotis2023icml-gradient,
title = {{Gradient Descent Converges Linearly for Logistic Regression on Separable Data}},
author = {Axiotis, Kyriakos and Sviridenko, Maxim},
booktitle = {International Conference on Machine Learning},
year = {2023},
pages = {1302-1319},
volume = {202},
url = {https://mlanthology.org/icml/2023/axiotis2023icml-gradient/}
}