An Investigation of Newton-Sketch and Subsampled Newton Methods
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The concepts of sketching and subsampling have recently received much attention by the optimization and statistics communities. In this paper, we study Newton-Sketch and Subsampled Newton (SSN) methods for the finite-sum optimization problem. We consider practical versions of the two methods in which the Newton equations are solved approximately using the conjugate gradient (CG) method or a stochastic gradient iteration. We establish new complexity results for the SSN-CG method that exploit the spectral properties of CG. Controlled numerical experiments compare the relative strengths of Newton-Sketch and SSN methods and show that for many finite-sum problems, they are far more efficient than SVRG, a popular first-order method.
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