Optimistic Rates for Learning with a Smooth Loss

Nathan Srebro; Karthik Sridharan; Ambuj Tewari

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arXiv · 1009.3896

Optimistic Rates for Learning with a Smooth Loss

Nathan Srebro·Karthik Sridharan·Ambuj Tewari

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Abstract

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

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Nathan Srebro, Karthik Sridharan, Ambuj Tewari. 2012-11-26. Optimistic Rates for Learning with a Smooth Loss. https://arxiv.org/abs/1009.3896

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