Optimal Learning

Name: Optimal Learning
Brand: Wiley
Price: 114.99 EUR
Availability: OnlineOnly

Warren B. Powell Ilya O. Ryzhov(Autor*in)

Wiley (Verlag)

Erschienen am 24. April 2012

404 Seiten

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Inhalt

Intro
Optimal Learning
CONTENTS
Preface
Acknowledgments
1 The Challenges of Learning
1.1 Learning the Best Path
1.2 Areas of Application
1.3 Major Problem Classes
1.4 The Different Types of Learning
1.5 Learning from Different Communities
1.6 Information Collection Using Decision Trees
1.6.1 A Basic Decision Tree
1.6.2 Decision Tree for Offline Learning
1.6.3 Decision Tree for Online Learning
1.6.4 Discussion
1.7 Website and Downloadable Software
1.8 Goals of this Book
Problems
2 Adaptive Learning
2.1 The Frequentist View
2.2 The Bayesian View
2.2.1 The Updating Equations for Independent Beliefs
2.2.2 The Expected Value of Information
2.2.3 Updating for Correlated Normal Priors
2.2.4 Bayesian Updating with an Uninformative Prior
2.3 Updating for Non-Gaussian Priors
2.3.1 The Gamma-Exponential Model
2.3.2 The Gamma-Poisson Model
2.3.3 The Pareto-Uniform Model
2.3.4 Models for Learning Probabilities*
2.3.5 Learning an Unknown Variance*
2.4 Monte Carlo Simulation
2.5 Why Does It Work?*
2.5.1 Derivation of s
2.5.2 Derivation of Bayesian Updating Equations for Independent Beliefs
2.6 Bibliographic Notes
Problems
3 The Economics of Information
3.1 An Elementary Information Problem
3.2 The Marginal Value of Information
3.3 An information Acquisition Problem
3.4 Bibliographic Notes
Problems
4 Ranking and Selection
4.1 The Model
4.2 Measurement Policies
4.2.1 Deterministic Versus Sequential Policies
4.2.2 Optimal Sequential Policies
4.2.3 Heuristic Policies
4.3 Evaluating Policies
4.4 More Advanced Topics*
4.4.1 An Alternative Representation of the Probability Space
4.4.2 Equivalence of Using True Means and Sample Estimates
4.5 Bibliographic Notes
Problems
5 The Knowledge Gradient
5.1 The Knowledge Gradient for Independent Beliefs
5.1.1 Computation
5.1.2 Some Properties of the Knowledge Gradient
5.1.3 The Four Distributions of Learning
5.2 The Value of Information and the S-Curve Effect
5.3 Knowledge Gradient for Correlated Beliefs
5.4 Anticipatory Versus Experiential Learning
5.5 The Knowledge Gradient for Some Non-Gaussian Distributions
5.5.1 The Gamma-Exponential Model
5.5.2 The Gamma-Poisson Model
5.5.3 The Pareto-Uniform Model
5.5.4 The Beta-Bernoulli Model
5.5.5 Discussion
5.6 Relatives of the Knowledge Gradient
5.6.1 Expected Improvement
5.6.2 Linear Loss*
5.7 The Problem of Priors
5.8 Discussion
5.9 Why Does It Work?*
5.9.1 Derivation of the Knowledge Gradient Formula
5.10 Bibliographic Notes
Problems
6 Bandit Problems
6.1 The Theory and Practice of Gittins Indices
6.1.1 Gittins Indices in the Beta-Bernoulli Model
6.1.2 Gittins Indices in the Normal-Normal Model
6.1.3 Approximating Gittins Indices
6.2 Variations of Bandit Problems
6.3 Upper Confidence Bounding
6.4 The Knowledge Gradient for Bandit Problems
6.4.1 The Basic Idea
6.4.2 Some Experimental Comparisons
6.4.3 Non-Normal Models
6.5 Bibliographic Notes
Problems
7 Elements of a Learning Problem
7.1 The States of our System
7.2 Types of Decisions
7.3 Exogenous Information
7.4 Transition Functions
7.5 Objective Functions
7.5.1 Designing Versus Controlling
7.5.2 Measurement Costs
7.5.3 Objectives
7.6 Evaluating Policies
7.7 Discussion
7.8 Bibliographic Notes
Problems
8 Linear Belief Models
8.1 Applications
8.1.1 Maximizing Ad Clicks
8.1.2 Dynamic Pricing
8.1.3 Housing Loans
8.1.4 Optimizing Dose Response
8.2 A Brief Review of Linear Regression
8.2.1 The Normal Equations
8.2.2 Recursive Least Squares
8.2.3 A Bayesian Interpretation
8.2.4 Generating a Prior
8.3 The Knowledge Gradient for a Linear Model
8.4 Application to Drug Discovery
8.5 Application to Dynamic Pricing
8.6 Bibliographic Notes
Problems
9 Subset Selection Problems
9.1 Applications
9.2 Choosing a Subset Using Ranking and Selection
9.2.1 Setting Prior Means and Variances
9.2.2 Two Strategies for Setting Prior Covariances
9.3 Larger Sets
9.3.1 Using Simulation to Reduce the Problem Size
9.3.2 Computational Issues
9.3.3 Experiments
9.4 Very Large Sets
9.5 Bibliographic Notes
Problems
10 Optimizing a Scalar Function
10.1 Deterministic Measurements
10.2 Stochastic Measurements
10.2.1 The Model
10.2.2 Finding the Posterior Distribution
10.2.3 Choosing the Measurement
10.2.4 Discussion
10.3 Bibliographic Notes
Problems
11 Optimal Bidding
11.1 Modeling Customer Demand
11.1.1 Some Valuation Models
11.1.2 The Logit Model
11.2 Bayesian Modeling for Dynamic Pricing
11.2.1 A Conjugate Prior for Choosing Between Two Demand Curves
11.2.2 Moment Matching for Nonconjugate Problems
11.2.3 An Approximation for the Logit Model
11.3 Bidding Strategies
11.3.1 An Idea From Multi-Armed Bandits
11.3.2 Bayes-Greedy Bidding
11.3.3 Numerical Illustrations
11.4 Why Does It Work?*
11.4.1 Moment Matching for Pareto Prior
11.4.2 Approximating the Logistic Expectation
11.5 Bibliographic Notes
Problems
12 Stopping Problems
12.1 Sequential Probability Ratio Test
12.2 The Secretary Problem
12.2.1 Setup
12.2.2 Solution
12.3 Bibliographic Notes
Problems
13 Active Learning in Statistics
13.1 Deterministic Policies
13.2 Sequential Policies for Classification
13.2.1 Uncertainty Sampling
13.2.2 Query by Committee
13.2.3 Expected Error Reduction
13.3 A Variance-Minimizing Policy
13.4 Mixtures of Gaussians
13.4.1 Estimating Parameters
13.4.2 Active Learning
13.5 Bibliographic Notes
14 Simulation Optimization
14.1 Indifference Zone Selection
14.1.1 Batch Procedures
14.1.2 Sequential Procedures
14.1.3 The 0-1 Procedure: Connection to Linear Loss
14.2 Optimal Computing Budget Allocation
14.2.1 Indifference-Zone Version
14.2.2 Linear Loss Version
14.2.3 When Does It Work?
14.3 Model-Based Simulated Annealing
14.4 Other Areas of Simulation Optimization
14.5 Bibliographic Notes
15 Learning in Mathematical Programming
15.1 Applications
15.1.1 Piloting a Hot Air Balloon
15.1.2 Optimizing a Portfolio
15.1.3 Network Problems
15.2 Learning on Graphs
15.3 Alternative Edge Selection Policies
15.4 Learning Costs for Linear Programs*
15.5 Bibliographic Notes
16 Optimizing Over Continuous Measurements
16.1 The Belief Model
16.1.1 Updating Equations
16.1.2 Parameter Estimation
16.2 Sequential Kriging Optimization
16.3 The Knowledge Gradient for Continuous Parameters*
16.3.1 Maximizing the Knowledge Gradient
16.3.2 Approximating the Knowledge Gradient
16.3.3 The Gradient of the Knowledge Gradient
16.3.4 Maximizing the Knowledge Gradient
16.3.5 The KGCP Policy
16.4 Efficient Global Optimization
16.5 Experiments
16.6 Extension to Higher-Dimensional Problems
16.7 Bibliographic Notes
17 Learning With a Physical State
17.1 Introduction to Dynamic Programming
17.1.1 Approximate Dynamic Programming
17.1.2 The Exploration vs. Exploitation Problem
17.1.3 Discussion
17.2 Some Heuristic Learning Policies
17.3 The Local Bandit Approximation
17.4 The Knowledge Gradient in Dynamic Programming
17.4.1 Generalized Learning Using Basis Functions
17.4.2 The Knowledge Gradient
17.4.3 Experiments
17.5 An Expected Improvement Policy
17.6 Bibliographic Notes
Index

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