Wasserstein PAC-Bayes Learning: A Bridge Between Generalisation and Optimisation. (arXiv:2304.07048v1 [stat.ML])

PAC-Bayes learning is an established framework to assess the generalisation
ability of learning algorithm during the training phase. However, it remains
challenging to know whether PAC-Bayes is useful to understand, before training,
why the output of well-known algorithms generalise well. We positively answer
this question by expanding the \emph{Wasserstein PAC-Bayes} framework, briefly
introduced in \cite{amit2022ipm}. We provide new generalisation bounds
exploiting geometric assumptions on the loss function. Using our framework, we
prove, before any training, that the output of an …

algorithm algorithms arxiv assumptions bayes bridge framework function loss optimisation training