Generalisation Under Gradient Descent via Deterministic PAC-Bayes
Abstract
We establish disintegrated PAC-Bayesian generalisation bounds for models trained with gradient descent methods or continuous gradient flows. Contrary to standard practice in the PAC-Bayesian setting, our result applies to optimisation algorithms that are deterministic, without requiring any de-randomisation step. Our bounds are fully computable, depending on the density of the initial distribution and the Hessian of the training objective over the trajectory. We show that our framework can be applied to a variety of iterative optimisation algorithms, including stochastic gradient descent (SGD), momentum-based schemes, and damped Hamiltonian dynamics.
Cite
Text
Clerico et al. "Generalisation Under Gradient Descent via Deterministic PAC-Bayes." Proceedings of The 36th International Conference on Algorithmic Learning Theory, 2025.Markdown
[Clerico et al. "Generalisation Under Gradient Descent via Deterministic PAC-Bayes." Proceedings of The 36th International Conference on Algorithmic Learning Theory, 2025.](https://mlanthology.org/alt/2025/clerico2025alt-generalisation/)BibTeX
@inproceedings{clerico2025alt-generalisation,
title = {{Generalisation Under Gradient Descent via Deterministic PAC-Bayes}},
author = {Clerico, Eugenio and Farghly, Tyler and Deligiannidis, George and Guedj, Benjamin and Doucet, Arnaud},
booktitle = {Proceedings of The 36th International Conference on Algorithmic Learning Theory},
year = {2025},
pages = {349-389},
volume = {272},
url = {https://mlanthology.org/alt/2025/clerico2025alt-generalisation/}
}