Second-Order Stochastic Optimization for Machine Learning in Linear Time
This addresses the efficiency bottleneck for large-scale machine learning optimization, enabling faster convergence with practical computational costs.
The paper tackles the problem of high computational cost in second-order stochastic optimization for machine learning by developing a method that matches the per-iteration cost of first-order gradient methods, with improvements in overall running time in some settings and linear-time implementation for sparse data.
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.