Introduction to Stochastic Search and Optimization Estimation, Simulation, and Control

ISBN-10: 0471330523

ISBN-13: 9780471330523

Edition: 2003

Authors: James C. Spall

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Spall presents a graduate-level introduction to the principles and algorithms of stochastic optimization. It is a strongly interdisciplinary book with potential and actual applications of the material in branches of mathematics, engineering, science and social sciences.
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Book details

List price: $192.00
Copyright year: 2003
Publisher: John Wiley & Sons, Incorporated
Publication date: 4/9/2003
Binding: Hardcover
Pages: 618
Size: 7.25" wide x 10.25" long x 1.25" tall
Weight: 2.838
Language: English

Stochastic Search and Optimization: Motivation and Supporting Results
General Background
Formal Problem Statement; General Types of Problems and Solutions; Global versus Local Search
Meaning of "Stochastic" in Stochastic Search and Optimization
Some Principles of Stochastic Search and Optimization
Some Key Points
Limits of Performance: No Free Lunch Theorems
Gradients, Hessians, and Their Connection to Optimization of "Smooth" Functions
Definition of Gradient and Hessian in the Context of Loss Functions
First- and Second-Order Conditions for Optimization
Deterministic Search and Optimization: Steepest Descent and Newton-Raphson Search
Steepest Descent Method
Newton-Raphson Method and Deterministic Convergence Rates
Concluding Remarks
Direct Methods for Stochastic Search
Random Search with Noise-Free Loss Measurements
Some Attributes of Direct Random Search
Three Algorithms for Random Search
Example Implementations
Random Search with Noisy Loss Measurements
Nonlinear Simplex (Nelder-Mead) Algorithm
Basic Method
Adaptation for Noisy Loss Measurements
Concluding Remarks
Recursive Estimation for Linear Models
Formulation for Estimation with Linear Models
Linear Model
Mean-Squared and Least-Squares Estimation
Least-Mean-Squares and Recursive-Least-Squares for Static [theta]
Basic LMS Algorithm
LMS Algorithm in Adaptive Signal Processing and Control
Basic RLS Algorithm
Connection of RLS to the Newton-Raphson Method
Extensions to Multivariate RLS and Weighted Summands in Least-Squares Criterion
LMS, RLS, and Kalman Filter for Time-Varying [theta]
Kalman Filter
Case Study: Analysis of Oboe Reed Data
Concluding Remarks
Stochastic Approximation for Nonlinear Root-Finding
Potpourri of Stochastic Approximation Examples
Convergence of Stochastic Approximation
Convergence Conditions
On the Gain Sequence and Connection to ODEs
Asymptotic Normality and Choice of Gain Sequence
Extensions to Basic Stochastic Approximation
Joint Parameter and State Evolution
Adaptive Estimation and Higher-Order Algorithms
Iterate Averaging
Time-Varying Functions
Concluding Remarks
Stochastic Gradient Form of Stochastic Approximation
Root-Finding Stochastic Approximation as a Stochastic Gradient Method
Basic Principles
Stochastic Gradient Algorithm
Implementation in General Nonlinear Regression Problems
Connection of LMS to Stochastic Gradient SA
Neural Network Training
Discrete-Event Dynamic Systems
Image Restoration
Concluding Remarks
Stochastic Approximation and the Finite-Difference Method
Introduction and Contrast of Gradient-Based and Gradient-Free Algorithms
Some Motivating Examples for Gradient-Free Stochastic Approximation
Finite-Difference Algorithm
Convergence Theory
Bias in Gradient Estimate
Asymptotic Normality
Practical Selection of Gain Sequences
Several Finite-Difference Examples
Some Extensions and Enhancements to the Finite-Difference Algorithm
Concluding Remarks
Simultaneous Perturbation Stochastic Approximation
Form and Motivation for Standard SPSA Algorithm
Basic Algorithm
Relationship of Gradient Estimate to True Gradient
Basic Assumptions and Supporting Theory for Convergence
Asymptotic Normality and Efficiency Analysis
Practical Implementation
Step-by-Step Implementation
Choice of Gain Sequences
Numerical Examples
Some Extensions: Optimal Perturbation Distribution; One-Measurement Form; Global, Discrete, and Constrained Optimization
Adaptive SPSA
Introduction and Basic Algorithm
Implementation Aspects of Adaptive SPSA
Theory on Convergence and Efficiency of Adaptive SPSA
Concluding Remarks
Appendix: Conditions for Asymptotic Normality
Annealing-Type Algorithms
Introduction to Simulated Annealing and Motivation from the Physics of Cooling
Simulated Annealing Algorithm
Basic Algorithm
Modifications for Noisy Loss Function Measurements
Some Examples
Global Optimization via Annealing Algorithms Based on Stochastic Approximation
Concluding Remarks
Appendix: Convergence Theory for Simulated Annealing Based on Stochastic Approximation
Evolutionary Computation I: Genetic Algorithms
Some Historical Perspective and Motivating Applications
Brief History
Early Motivation
Coding of Elements for Searching
Standard Bit Coding
Gray Coding
Real-Number Coding
Standard Genetic Algorithm Operations
Selection and Elitism
Mutation and Termination
Overview of Basic GA Search Approach
Practical Guidance and Extensions: Coefficient Values, Constraints, Noisy Fitness Evaluations, Local Search, and Parent Selection
Concluding Remarks
Evolutionary Computation II: General Methods and Theory
Overview of Evolution Strategy and Evolutionary Programming with Comparisons to Genetic Algorithms
Schema Theory
What Makes a Problem Hard?
Convergence Theory
No Free Lunch Theorems
Concluding Remarks
Reinforcement Learning via Temporal Differences
Delayed Reinforcement and Formulation for Temporal Difference Learning
Basic Temporal Difference Algorithm
Batch and Online Implementations of TD Learning
Some Examples
Connections to Stochastic Approximation
Concluding Remarks
Statistical Methods for Optimization in Discrete Problems
Introduction to Multiple Comparisons Over a Finite Set
Statistical Comparisons Test Without Prior Information
Multiple Comparisons Against One Candidate with Known Noise Variance(s)
Multiple Comparisons Against One Candidate with Unknown Noise Variance(s)
Extensions to Bonferroni Inequality; Ranking and Selection Methods in Optimization Over a Finite Set
Concluding Remarks
Model Selection and Statistical Information
Bias-Variance Tradeoff
Bias and Variance as Contributors to Model Prediction Error
Interpretation of the Bias-Variance Tradeoff
Bias-Variance Analysis for Linear Models
Model Selection: Cross-Validation
The Information Matrix: Applications and Resampling-Based Computation
Fisher Information Matrix: Definition and Two Equivalent Forms
Two Key Properties of the Information Matrix: Connections to the Covariance Matrix of Parameter Estimates
Selected Applications
Resampling-Based Calculation of the Information Matrix
Concluding Remarks
Simulation-Based Optimization I: Regeneration, Common Random Numbers, and Selection Methods
Focus of Chapter and Roles of Search and Optimization in Simulation
Statement of the Optimization Problem
Regenerative Systems
Background and Definition of the Loss Function L([theta])
Estimators of L([theta])
Estimates Related to the Gradient of L([theta])
Optimization with Finite-Difference and Simultaneous Perturbation Gradient Estimators
Common Random Numbers
Theory and Examples for Common Random Numbers
Partial Common Random Numbers for Finite Samples
Selection Methods for Optimization with Discrete-Valued [theta]
Concluding Remarks
Simulation-Based Optimization II: Stochastic Gradient and Sample Path Methods
Framework for Gradient Estimation
Some Issues in Gradient Estimation
Gradient Estimation and the Interchange of Derivative and Integral
Pure Likelihood Ratio/Score Function and Pure Infinitesimal Perturbation Analysis
Gradient Estimation Methods in Root-Finding Stochastic Approximation: The Hybrid LR/SF and IPA Setting
Sample Path Optimization
Concluding Remarks
Markov Chain Monte Carlo
Metropolis-Hastings Algorithm
Gibbs Sampling
Sketch of Theoretical Foundation for Gibbs Sampling
Some Examples of Gibbs Sampling
Applications in Bayesian Analysis
Concluding Remarks
Optimal Design for Experimental Inputs
Finite-Sample and Asymptotic (Continuous) Designs
Precision Matrix and D-Optimality
Linear Models
Background and Connections to D-Optimality
Some Properties of Asymptotic Designs
Orthogonal Designs
Sketch of Algorithms for Finding Optimal Designs
Response Surface Methodology
Nonlinear Models
Methods for Coping with Dependence on [theta]
Concluding Remarks
Appendix: Optimal Design in Dynamic Models
Selected Results from Multivariate Analysis
Multivariate Calculus and Analysis
Some Useful Results in Matrix Theory
Some Basic Tests in Statistics
Standard One-Sample Test
Some Basic Two-Sample Tests
Comments on Other Aspects of Statistical Testing
Probability Theory and Convergence
Basic Properties
Convergence Theory
Definitions of Convergence
Examples and Counterexamples Related to Convergence
Dominated Convergence Theorem
Convergence in Distribution and Central Limit Theorem
Random Number Generation
Background and Introduction to Linear Congruential Generators
Transformation of Uniform Random Numbers to Other Distributions
Markov Processes
Background on Markov Processes
Discrete Markov Chains
Answers to Selected Exercises
Frequently Used Notation
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