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In supervised learning using kernel methods, we often encounter a large-scalefinite-sum minimization over a reproducing kernel Hilbert space (RKHS).Large-scale finite-sum problems can be solved using efficient variants ofNewton method, where the Hessian is approximated via sub-samples of data. InRKHS, however, the dependence of the penalty function to kernel makes standardsub-sampling approaches inapplicable, since the gram matrix is not readilyavailable in a low-rank form. In this paper, we observe that for this class ofproblems, one can naturally use kernel approximation to speed up the Newtonmethod. Focusing on randomized features for kernel approximation, we provide anovel second-order algorithm that enjoys local superlinear convergence andglobal linear convergence (with high probability). We derive the theoreticallower bound for the number of random features required for the approximatedHessian to be close to the true Hessian in the norm sense. Our numericalexperiments on real-world data verify the efficiency of our method compared toseveral benchmarks.

RFN: A Random-Feature Based Newton Method for Empirical Risk Minimization in Reproducing Kernel Hilbert Spaces