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An Investigation of Newton-Sketch and Subsampled Newton Methods

Albert S. Berahas (albertberahas***at***u.northwestern.edu)
Raghu Bollapragada (raghu.bollapragada***at***u.northwestern.edu)
Jorge Nocedal (j-nocedal***at***northwestern.edu)

Abstract: 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.

Keywords: Subsampling, Sketching, Machine Learning, Newton Methods

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization

Category 3: Stochastic Programming

Citation: Northwestern University, May 2017

Download: [PDF]

Entry Submitted: 05/17/2017
Entry Accepted: 05/17/2017
Entry Last Modified: 05/18/2017

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