Secant Line Search for Frank-Wolfe Algorithms
Abstract
We present a new step-size strategy based on the secant method for Frank-Wolfe algorithms. This strategy, which requires mild assumptions about the function under consideration, can be applied to any Frank-Wolfe algorithm. It is as effective as full line search and, in particular, allows for adapting to the local smoothness of the function, such as in (Pedregosa et al., 2020), but comes with a significantly reduced computational cost, leading to higher effective rates of convergence. We provide theoretical guarantees and demonstrate the effectiveness of the strategy through numerical experiments.
Cite
Text
Hendrych et al. "Secant Line Search for Frank-Wolfe Algorithms." Proceedings of the 42nd International Conference on Machine Learning, 2025.Markdown
[Hendrych et al. "Secant Line Search for Frank-Wolfe Algorithms." Proceedings of the 42nd International Conference on Machine Learning, 2025.](https://mlanthology.org/icml/2025/hendrych2025icml-secant/)BibTeX
@inproceedings{hendrych2025icml-secant,
title = {{Secant Line Search for Frank-Wolfe Algorithms}},
author = {Hendrych, Deborah and Pokutta, Sebastian and Besançon, Mathieu and Martı́nez-Rubio, David},
booktitle = {Proceedings of the 42nd International Conference on Machine Learning},
year = {2025},
pages = {23005-23029},
volume = {267},
url = {https://mlanthology.org/icml/2025/hendrych2025icml-secant/}
}