Fast Rates for Regularized Objectives
karthik Sridharan, Shai Shalev-Shwartz and Nathan Srebro
In: NIPS 2008, Dec 2008, Vancouver.
We show that the empirical minimizer of a stochastic strongly convex
objective, where the stochastic component is linear, converges to the
population minimizer with rate $O(1/n)$. The result applies, in
particular, to the SVM objective. Thus, we obtain a rate of $O(1/n)$ on
the convergence of the SVM objective to its infinite data limit. We
demonstrate how this is essential for obtaining tight oracle
inequalities for SVMs. The results extend also to strong convexity
with respect to other norms, and so also to objectives
regularized using other $\ellnorm_p$ norms.