Cautious Optimizers: Improving Training with One Line of Code

ICLR 2026 Conference Submission14690 Authors

Keywords: Optimizer, AdamW

TL;DR: Improving Training with One Line of Code

Abstract: AdamW has been the default optimizer for transformer pretraining. For many years, our community searched for faster and more stable optimizers with only constrained positive outcomes. In this work, we propose a \textbf{single-line modification in Pytorch} to any momentum-based optimizer, which we rename cautious optimizer, e.g. C-AdamW and C-Lion. Our theoretical result shows that this modification preserves Adam's Hamiltonian function and it does not break the convergence guarantee under the Lyapunov analysis. In addition, a whole new family of optimizers is revealed by our theoretical insight. Among them, we pick the simplest one for empirical experiments, showing not only consistent speed-up on LLM pretraining and post-training tasks, but also better results in MAE pretraining, with minimum extra tuning on hyperparameters.

Primary Area: foundation or frontier models, including LLMs

Submission Number: 14690