Smoothness, Low-Noise and Fast Rates
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Abstract
We establish an excess risk bound of 
for ERM with an H-smooth loss function and a hypothesis class with Rademacher complexity 
, where 
is the best risk achievable by the hypothesis class. For typical hypothesis classes where 
this translates to a learning rate of 
in the separable 
case and 
generally. We also provide similar guarantees for online and stochastic convex optimization of a smooth non-negative objective.
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