We discuss necessary conditions for a PAC-Bayes bound to provide a meaningful generalisation guarantee. Our analysis reveals that the optimal generalisation guarantee depends solely on the distribution of the risk induced by the prior distribution. In particular, achieving a target generalisation level is only achievable if the prior places sufficient mass on high-performing predictors. We relate these requirements to the prevalent practice of using data-dependent priors in deep learning PAC-Bayes applications, and discuss the implications for the claim that PAC-Bayes ``explains'' generalisation.
View on arXiv@article{picard-weibel2025_2503.08231,
title={ How good is PAC-Bayes at explaining generalisation? },
author={ Antoine Picard-Weibel and Eugenio Clerico and Roman Moscoviz and Benjamin Guedj },
journal={arXiv preprint arXiv:2503.08231},
year={ 2025 }
}