Exact and Inexact Subsampled Newton Methods for Optimization
| Autor: | Richard H. Byrd, Raghu Bollapragada, Jorge Nocedal |
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| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Hessian matrix
FOS: Computer and information sciences Applied Mathematics General Mathematics Linear system ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION MathematicsofComputing_NUMERICALANALYSIS Machine Learning (stat.ML) 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Computational Mathematics symbols.namesake Rate of convergence Optimization and Control (math.OC) Statistics - Machine Learning Conjugate gradient method symbols FOS: Mathematics Applied mathematics Stochastic optimization 0101 mathematics Newton's method Mathematics - Optimization and Control Mathematics |
| Popis: | The paper studies the solution of stochastic optimization problems in which approximations to the gradient and Hessian are obtained through subsampling. We first consider Newton-like methods that employ these approximations and discuss how to coordinate the accuracy in the gradient and Hessian to yield a superlinear rate of convergence in expectation. The second part of the paper analyzes an inexact Newton method that solves linear systems approximately using the conjugate gradient (CG) method, and that samples the Hessian and not the gradient (the gradient is assumed to be exact). We provide a complexity analysis for this method based on the properties of the CG iteration and the quality of the Hessian approximation, and compare it with a method that employs a stochastic gradient iteration instead of the CG method. We report preliminary numerical results that illustrate the performance of inexact subsampled Newton methods on machine learning applications based on logistic regression. 37 pages |
| Databáze: | OpenAIRE |
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