Reviews: Fast learning rates with heavy-tailed losses

This paper provides some new results in an important area which is receiving more and more attention: fast rates when loss functions are unbounded and heavy-tailed. Existing results based on empirical process theory often rely on bounded or sub-Gaussian loss, and the heavy tails (hence non-sub-Gaussian) case is considerably harder. The results presented seem sound and are definitely novel. They rely on results of Sara van de Geer and collaborators on concentration inequalities for unbounded empirical processes. The material is very technical and I would suggest moving even some more material to the appendix.