This paper contains a recipe for deriving new PAC-Bayes generalisation bounds based on the $(f, \Gamma)$-divergence, and, in addition, presents PAC-Bayes generalisation bounds where we interpolate between a series of probability divergences (including but not limited to KL, Wasserstein, and total variation), making the best out of many worlds depending on the posterior distributions properties. We explore the tightness of these bounds and connect them to earlier results from statistical learning, which are specific cases. We also instantiate our bounds as training objectives, yielding non-trivial guarantees and practical performances.

翻译：本文提出了一种基于$(f, \Gamma)$-散度推导新PAC-Bayes泛化界的方法，并进一步给出了在多个概率散度（包括但不限于KL散度、Wasserstein散度及全变差散度）之间进行插值的PAC-Bayes泛化界。这些新界能够根据后验分布的特性，从多种散度中择优而用。我们探讨了这些界的紧致性，并将其与统计学习中的已有结果（作为特例）建立联系。此外，我们还将所提出的界实例化为训练目标，从而获得非平凡的理论保证与实用性能。