Wasserstein PAC-Bayes Learning: A Bridge Between Generalisation and Optimisation
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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 Wasserstein PAC-Bayes framework, briefly introduced in <cit.>. 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 from <cit.> has a strong asymptotic generalisation ability. More precisely, we show that it is possible to incorporate optimisation results within a generalisation framework, building a bridge between PAC-Bayes and optimisation algorithms.
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