Book contents
- Frontmatter
- Contents
- Acknowledgements
- List of contributors
- Foreword
- 1 Introduction
- 2 On-line Learning and Stochastic Approximations
- 3 Exact and Perturbation Solutions for the Ensemble Dynamics
- 4 A Statistical Study of On-line Learning
- 5 On-line Learning in Switching and Drifting Environments with Application to Blind Source Separation
- 6 Parameter Adaptation in Stochastic Optimization
- 7 Optimal On-line Learning in Multilayer Neural Networks
- 8 Universal Asymptotics in Committee Machines with Tree Architecture
- 9 Incorporating Curvature Information into On-line Learning
- 10 Annealed On-line Learning in Multilayer Neural Networks
- 11 On-line Learning of Prototypes and Principal Components
- 12 On-line Learning with Time-Correlated Examples
- 13 On-line Learning from Finite Training Sets
- 14 Dynamics of Supervised Learning with Restricted Training Sets
- 15 On-line Learning of a Decision Boundary with and without Queries
- 16 A Bayesian Approach to On-line Learning
- 17 Optimal Perceptron Learning: an On-line Bayesian Approach
6 - Parameter Adaptation in Stochastic Optimization
Published online by Cambridge University Press: 28 January 2010
- Frontmatter
- Contents
- Acknowledgements
- List of contributors
- Foreword
- 1 Introduction
- 2 On-line Learning and Stochastic Approximations
- 3 Exact and Perturbation Solutions for the Ensemble Dynamics
- 4 A Statistical Study of On-line Learning
- 5 On-line Learning in Switching and Drifting Environments with Application to Blind Source Separation
- 6 Parameter Adaptation in Stochastic Optimization
- 7 Optimal On-line Learning in Multilayer Neural Networks
- 8 Universal Asymptotics in Committee Machines with Tree Architecture
- 9 Incorporating Curvature Information into On-line Learning
- 10 Annealed On-line Learning in Multilayer Neural Networks
- 11 On-line Learning of Prototypes and Principal Components
- 12 On-line Learning with Time-Correlated Examples
- 13 On-line Learning from Finite Training Sets
- 14 Dynamics of Supervised Learning with Restricted Training Sets
- 15 On-line Learning of a Decision Boundary with and without Queries
- 16 A Bayesian Approach to On-line Learning
- 17 Optimal Perceptron Learning: an On-line Bayesian Approach
Summary
Abstract
Optimization is an important operation in many domains of science and technology. Local optimization techniques typically employ some form of iterative procedure, based on derivatives of the function to be optimized (objective function). These techniques normally involve parameters that must be set by the user, often by trial and error. Those parameters can have a strong influence on the convergence speed of the optimization. In several cases, a significant speed advantage could be gained if one could vary these parameters during the optimization, to reflect the local characteristics of the function being optimized. Some parameter adaptation methods have been proposed for this purpose, for deterministic optimization situations. For stochastic (also called on-line) optimization situations, there appears to be no simple and effective parameter adaptation method.
This paper proposes a new method for parameter adaptation in stochastic optimization. The method is applicable to a wide range of objective functions, as well as to a large set of local optimization techniques. We present the derivation of the method, details of its application to gradient descent and to some of its variants, and examples of its use in the gradient optimization of several functions, as well as in the training of a multilayer perceptron by on-line backpropagation.
Introduction
Optimization is an operation that is often used in several different domains of science and technology. It normally consists of maximizing or minimizing a given function (called objective function), that is chosen to represent the quality of a given system. The system may be physical, (mechanical, chemical, etc.), a mathematical model, a computer program, etc., or even a mixture of several of these.
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- On-Line Learning in Neural Networks , pp. 111 - 134Publisher: Cambridge University PressPrint publication year: 1999
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