Smoothness, Low-Noise and Fast Rates

Details Smoothness, Low-Noise and Fast Rates Smoothness, Low-Noise and Fast Rates

2010-09-20

arxiv.org/abs/1009.3896v1

Computer Science

Learning

Scientific paper

We establish am excess risk bound of order $H \Rad_n^2 + \sqrt{H L^*}\Rad_n$ for ERM with an H-smooth loss function and a hypothesis class with Rademacher complexity $\Rad_n$, where $L^*$ is the best risk achievable by the hypothesis class. For typical hypothesis classes where $\Rad_n = \sqrt{R/n}$, this translates to a learning rate of order $RH/n$ in the separable ($L^*=0$) case and $RH/n + \sqrt{L^* RH/n}$ more generally. We also provide similar guarantees for online and stochastic convex optimization of a smooth non-negative objective.

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