Introduction to Stochastic Dynamic Programming

Introduction to Stochastic Dynamic Programming

1st Edition - March 28, 1983

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  • Author: Sheldon Ross
  • eBook ISBN: 9781483269092

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Description

Introduction to Stochastic Dynamic Programming presents the basic theory and examines the scope of applications of stochastic dynamic programming. The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist—providing counterexamples where appropriate—and then presents methods for obtaining such policies when they do. In addition, general areas of application are presented. The final two chapters are concerned with more specialized models. These include stochastic scheduling models and a type of process known as a multiproject bandit. The mathematical prerequisites for this text are relatively few. No prior knowledge of dynamic programming is assumed and only a moderate familiarity with probability— including the use of conditional expectation—is necessary.

Table of Contents


  • Preface

    I. Finite-Stage Models

    1. Introduction

    2. A Gambling Model

    3. A Stock-Option Model

    4. Modular Functions and Monotone Policies

    5. Accepting the Best Offer

    6. A Sequential Allocation Model

    7. The Interchange Argument in Sequencing

    Problems

    Notes and References

    II. Discounted Dynamic Programming

    1. Introduction

    2. The Optimality Equation and Optimal Policy

    3. Method of Successive Approximations

    4. Policy Improvement

    5. Solution by Linear Programming

    6. Extension to Unbounded Rewards

    Problems

    References

    III. Minimizing Costs—Negative Dynamic Programming

    1. Introduction and Some Theoretical Results

    2. Optimal Stopping Problems

    3. Bayesian Sequential Analysis

    4. Computational Approaches

    5. Optimal Search

    Problems

    References

    IV. Maximizing Rewards—Positive Dynamic Programming

    1. Introduction and Main Theoretical Results

    2. Applications to Gambling Theory

    3. Computational Approaches to Obtaining V

    Problems

    Notes and References

    V. Average Reward Criterion

    1. Introduction and Counterexamples

    2. Existence of an Optimal Stationary Policy

    3. Computational Approaches

    Problems

    Notes and References

    VI. Stochastic Scheduling

    1. Introduction

    2. Maximizing Finite-Time Returns—Single Processor

    3. Minimizing Expected Makespan—Processors in Parallel

    4. Minimizing Expected Makespan—Processors in Series

    5. Maximizing Total Field Life

    6. A Stochastic Knapsack Model

    7. A Sequential-Assignment Problem

    Problems

    Notes and References

    VII. Bandit Processes

    1. Introduction

    2. Single-Project Bandit Processes

    3. Multiproject Bandit Processes

    4. An Extension and a Nonextension

    5. Generalizations of the Classical Bandit Problem

    Problems

    Notes and References

    Appendix: Stochastic Order Relations

    1. Stochastically Larger

    2. Coupling

    3. Hazard-Rate Ordering

    4. Likelihood-Ratio Ordering

    Problems

    Reference

    Index

Product details

  • No. of pages: 178
  • Language: English
  • Copyright: © Academic Press 1983
  • Published: March 28, 1983
  • Imprint: Academic Press
  • eBook ISBN: 9781483269092

About the Author

Sheldon Ross

Sheldon Ross
Dr. Sheldon M. Ross is a professor in the Department of Industrial and Systems Engineering at the University of Southern California. He received his PhD in statistics at Stanford University in 1968. He has published many technical articles and textbooks in the areas of statistics and applied probability. Among his texts are A First Course in Probability, Introduction to Probability Models, Stochastic Processes, and Introductory Statistics. Professor Ross is the founding and continuing editor of the journal Probability in the Engineering and Informational Sciences. He is a Fellow of the Institute of Mathematical Statistics, a Fellow of INFORMS, and a recipient of the Humboldt US Senior Scientist Award.

Affiliations and Expertise

Professor, Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, USA

About the Editors

Z. W. Birnbaum

E. Lukacs

Affiliations and Expertise

Bowling Green State University

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