We present a new high-probability PAC-Bayes oracle bound for unbounded
losses. This result can be understood as a PAC-Bayes version of the Chernoff
bound. The proof technique relies on uniformly bounding the tail of certain
random variable based on the Cram\'er transform of the loss. We highlight two
applications of our main result. First, we show that our bound solves the open
problem of optimizing the free parameter on many PAC-Bayes bounds. Finally, we
show that our approach allows working with flexible assumptions on the loss
function, resulting in novel bounds that generalize previous ones and can be
minimized to obtain Gibbs-like posteriors.

我们提出了一个新的高概率 PAC-Bayes 预言界，用于无界损失。该结果可以理解为 Chernoff 界的 PAC-Bayes 版本。证明技巧依赖于基于损失的 Cramé 变换来统一地对某些随机变量的尾部进行界定。我们强调了我们主要结果的两个应用。首先，我们展示了我们的界解决了许多 PAC-Bayes 界上优化自由参数的开放问题。最后，我们展示了我们的方法允许在损失函数上进行灵活的假设，从而得到泛化之前界的新界，并且可以最小化以获取类似于 Gibbs 的后验概率。