A Quasi-Newton Method for Large Scale Support Vector Machines

Abstract

This paper adapts a recently developed regularized stochastic version of the Broyden, Fletcher, Goldfarb, and Shanno (BFGS) quasi-Newton method for the solution of support vector machine classification problems. The proposed method is shown to converge almost surely to the optimal classifier at a rate that is linear in expectation. Numerical results show that the proposed method exhibits a convergence rate that degrades smoothly with the dimensionality of the feature vectors.