A PAC-Bayes bound for deterministic classifiers. (arXiv:2209.02525v2 [stat.ML] UPDATED)

We establish a disintegrated PAC-Bayesian bound, for classifiers that are
trained via continuous-time (non-stochastic) gradient descent. Contrarily to
what is standard in the PAC-Bayesian setting, our result applies to a training
algorithm that is deterministic, conditioned on a random initialisation,
without requiring any $\textit{de-randomisation}$ step. We provide a broad
discussion of the main features of the bound that we propose, and we study
analytically and empirically its behaviour on linear models, finding promising
results.

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