In this paper, we present new high-probability PAC-Bayes bounds for different
types of losses. Firstly, for losses with a bounded range, we present a
strengthened version of Catoni's bound that holds uniformly for all parameter
values. This leads to new fast rate and mixed rate bounds that are
interpretable and tighter than previous bounds in the literature. Secondly, for
losses with more general tail behaviors, we introduce two new parameter-free
bounds: a PAC-Bayes Chernoff analogue when the loss' cumulative generating
function is bounded, and a bound when the loss' second moment is bounded. These
two bounds are obtained using a new technique based on a discretization of the
space of possible events for the "in probability" parameter optimization
problem. Finally, we extend all previous results to anytime-valid bounds using
a simple technique applicable to any existing bound.

该论文提出了一种新的高概率 PAC-Bayes 界限，其中涉及到了带界范围和更一般尾部行为的损失，并提出了一些新的基于参数和基于事件的界限技术，可以得到更紧密和可解释的结果，并将结果扩展到任何现有范围上