The fundamental theorem of statistical learning gives an equivalence between uniform convergence of the empirical risk to learning in the PAC framework.
I have only seen this stated in the case of binary classification with the 0-1 loss. Does a result of this form hold in more general settings? For example: margin-based classification rules, regression, multi-class classification, ...?
Another statement of this question could be: under what circumstances does uniform convergence of the empirical risk imply PAC learning? (I am most interested in this direction of implication.)
Please provide references if you have them.