The Surprising Agreement Between Convex Optimization Theory and Learning-Rate Scheduling for Large Model Training
Fabian Schaipp, Alexander Hägele, Adrien Taylor, Umut Simsekli, Francis Bach
Abstract
We show that learning-rate schedules for large model training behave surprisingly similar to a performance bound from non-smooth convex optimization theory. We provide a bound for the constant schedule with linear cooldown; in particular, the practical benefit of cooldown is reflected in the bound due to the absence of logarithmic terms. Further, we show that this surprisingly close match between optimization theory and practice can be exploited for learning-rate tuning: we achieve noticeable improvements for training 124M and 210M Llama-type models by (i) extending the schedule for continued training with optimal learning-rate, and (ii) transferring the optimal learning-rate across schedules.
BibTeX
@inproceedings{
schaipp2025the,
title={The Surprising Agreement Between Convex Optimization Theory and Learning-Rate Scheduling for Large Model Training},
author={Fabian Schaipp and Alexander H{\"a}gele and Adrien Taylor and Umut Simsekli and Francis Bach},
booktitle={Forty-second International Conference on Machine Learning},
year={2025},
url={https://openreview.net/forum?id=b836TGkRSw}
}