Secant Line Search for Frank-Wolfe Algorithms

Deborah Hendrych, Sebastian Pokutta, Mathieu Besançon, David Martı́nez-Rubio
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:23005-23029, 2025.

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 this Paper

BibTeX
@InProceedings{pmlr-v267-hendrych25a, title = {Secant Line Search for Frank-{W}olfe Algorithms}, author = {Hendrych, Deborah and Pokutta, Sebastian and Besan\c{c}on, Mathieu and Mart\'{\i}nez-Rubio, David}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {23005--23029}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/hendrych25a/hendrych25a.pdf}, url = {https://proceedings.mlr.press/v267/hendrych25a.html}, 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.} }
Endnote
%0 Conference Paper %T Secant Line Search for Frank-Wolfe Algorithms %A Deborah Hendrych %A Sebastian Pokutta %A Mathieu Besançon %A David Martı́nez-Rubio %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-hendrych25a %I PMLR %P 23005--23029 %U https://proceedings.mlr.press/v267/hendrych25a.html %V 267 %X 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.
APA
Hendrych, D., Pokutta, S., Besançon, M. & Martı́nez-Rubio, D.. (2025). Secant Line Search for Frank-Wolfe Algorithms. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:23005-23029 Available from https://proceedings.mlr.press/v267/hendrych25a.html.

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