The developments of Rademacher complexity and PAC-Bayesian theory have been
largely independent. One exception is the PAC-Bayes theorem of Kakade,
Sridharan, and Tewari (2008), which is established via Rademacher complexity
theory by viewing Gibbs classifiers as linear operators. The goal of this paper
is to extend this bridge between Rademacher complexity and state-of-the-art
PAC-Bayesian theory. We first demonstrate that one can match the fast rate of
Catoni's PAC-Bayes bounds (Catoni, 2007) using shifted Rademacher processes
(Wegkamp, 2003; Lecu\'{e} and Mitchell, 2012; Zhivotovskiy and Hanneke, 2018).
We then derive a new fast-rate PAC-Bayes bound in terms of the "flatness" of
the empirical risk surface on which the posterior concentrates. Our analysis
establishes a new framework for deriving fast-rate PAC-Bayes bounds and yields
new insights on PAC-Bayesian theory.

本文旨在扩展 Rademacher 复杂性和最新 PAC - 贝叶斯理论之间的桥梁，首先通过平移 Rademacher 过程来匹配 Catoni PAC-Bayes 界限的快速率，然后最新地导出了快速 PAC-Bayes 界限，重点是后验集中在的经验风险表面的 “平坦度”。