Before revision:  Although there exists plentiful generalization analysis of ERM and SGD for supervised learning, current theoretical understandings of ERM and SGD are either have stronger assumptions in convex learning, e.g., strong convexity condition , or show slow rates and less studied in nonconvex learning.
After revision:  Although there exists plentiful generalization analysis of ERM and SGD for supervised learning, current theoretical understandings of ERM and SGD either have stronger assumptions in convex learning, e.g., strong convexity condition , or show slow rates and less studied in nonconvex learning.