Localization of VC Classes: Beyond Local Rademacher Complexities
  In this paper we introduce an alternative localization approach for binary classification that leads to a novel complexity measure: fixed points of the local empirical entropy. We show that this complexity measure gives a tight control over complexity in the upper bounds. Our results are accompanied by a novel minimax lower bound that involves the same quantity. In particular, we practically answer the question of optimality of ERM under bounded noise for general VC classes. 
Nikita Zhivotovskiy and Steve Hanneke
math.ST stat.TH