Second-Order Stochastic Optimization for Machine Learning in Linear Time, Journal of Machine Learning Research(2017)
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to eﬃcient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored due to the high cost of computing the second-order information. In this paper we develop second-order stochastic methods for optimization problems in machine learning that match the per-iteration cost of gradient based methods, and in certain settings improve upon the overall running time over popular ﬁrst-order methods. Furthermore, our algorithm has the desirable property of being implementable in time linear in the sparsity of the input data.