Abstract
In this paper, a stochastic quasi-Newton algorithm for nonconvex stochastic optimization is presented. It is derived from a classical modified BFGS formula. The update formula can be extended to the framework of limited memory scheme. Numerical experiments on some problems in machine learning are given. The results show that the proposed algorithm has great prospects.
Highlights
IntroductionMachine learning is an interdisciplinary subject involving probability theory, statistics, approximation theory, convex analysis, algorithm complexity theory, and so on
We focus on the numerical performances of the proposed Algorithm 3 for solving nonconvex empirical risk minimization (ERM) problems and nonconvex support vector machine (SVM) problems
We present the numerical results of LMLBFGS-VR, SGD, SVRG, and SAGA for solving Problem 1 on the four data sets
Summary
Machine learning is an interdisciplinary subject involving probability theory, statistics, approximation theory, convex analysis, algorithm complexity theory, and so on. People usually construct an appropriate model from an extraordinary large amount of data. The traditional algorithms for solving optimization problems are no longer suitable for machine learning problems. A stochastic algorithm must be used to solve the model optimization problem we encounter in machine learning
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