I've recently came across topic known as PAC-Bayesian, but I cannot find a source to read about it. Any article that I came across are talking about its application in a specific area but there is no introduction to what it exactly is.
Here are a few quick Google hits...
- PAC-Bayes Analysis: Background and Applications
- Probably Approximately Correct Learning and Vapnik-Chervonenkis Dimension
- Probably approximately correct learning on Wikipedia
- Overview of the Probably Approximately Correct (PAC) Learning Framework
From this last one, a quote:
A more refined, Bayesian extension of the PAC model is explored in . Using the Bayesian approach involves assuming a prior distribution over possible target concepts as well as training instances. Given these distributions, the average error of the hypothesis as a function of training sample size, and even as a function of the particular training sample, can be defined. Also, $1 - \delta$ confidence intervals like those in the PAC model can be defined as well.
 $=$ W. Buntine, A Theory of Learning Classification Rules. PhD thesis, University of Technology, Sydney, 1990.
This paper is a good way to start : https://arxiv.org/pdf/1901.05353.pdf
A more recent elementary introduction to PAC-Bayes
by Pierre Alquier. It is an 80 page study of this topic.