I am starting to learn PAC learning, and have an interest in PAC-Bayes bound. However, most of the materials I found assumed binary classification only, while I am looking for the extension of PAC-Bayes bound for multiclass classification.
In chapter 3, section 3.2.2 of the textbook "Understanding machine learning: from theory to algorithms" written by Shalev-Shwartz and Ben-David, the multiclass classification is discussed and concluded with the definition of the Agnostic PAC learning for general loss function. However, I cannot find some basic extensions or proofs about multiclass classification for PAC-Bayes bound. The tutorial of PAC-Bayes bound by Langford (2005) is also about binary classification only.
I found the paper  interesting, but they use different performance measurement with the constrain that the minimum examples of a class $m \ge 8$. Would you like to suggest any papers or basic materials discussing PAC-Bayes bound for multiclass classification that extended some of the bounds used in binary classification such as ?
 Morvant, Emilie, Sokol Koço, and Liva Ralaivola. "PAC-Bayesian generalization bound on confusion matrix for multi-class classification." in International Conference on Machine Learning (2012).
 McAllester, David A. "PAC-Bayesian model averaging." Proceedings of the twelfth annual conference on Computational learning theory. ACM, 1999.