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Globally convergent stochastic optimization with optimal asymptotic distribution

Part of: Artificial intelligence (68Txx) Sequential methods

Published online by Cambridge University Press:  14 July 2016

Jürgen Dippon
Jürgen Dippon*
Affiliation:
Universität Stuttgart
*
∗ Postal address: Mathematisches Institut A, Universität Stuttgart, 70511 Stuttgart, Germany. E-mail address: dippon@mathematik.uni-stuttgart.de
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Abstract

A stochastic gradient descent method is combined with a consistent auxiliary estimate to achieve global convergence of the recursion. Using step lengths converging to zero slower than 1/n and averaging the trajectories, yields the optimal convergence rate of 1/√n and the optimal variance of the asymptotic distribution. Possible applications can be found in maximum likelihood estimation, regression analysis, training of artificial neural networks, and stochastic optimization.

Keywords

Stochastic approximationglobal stochastic optimizationaveraginggradient descentconsistencycentral limit theoremM-estimatormaximum likelihood estimationregression analysisartificial neural networks

MSC classification

Primary: 62L12: Sequential estimation 62L20: Stochastic approximation
Secondary: 68T05: Learning and adaptive systems 68T10: Pattern recognition, speech recognition

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 2 , June 1998 , pp. 395 - 406
Copyright
Copyright © Applied Probability Trust 1998 

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