Introduction to Stochastic Dynamic Programming

Sheldon M. Ross, Z. W. Birnbaum, E. Lukacs

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483269092
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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

• Front Cover
• Introduction to Stochastic Dynamic Programming
• Copyright Page
• Table of Contents
• Dedication
• Preface
• Chapter I. Finite-Stage Models
• Chapter II. Discounted Dynamic Programming
• Chapter III. Minimizing Costs—Negative Dynamic Programming
• Chapter IV. Maximizing Rewards—Positive Dynamic Programming
• Chapter V. Average Reward Criterion
• Chapter VI. Stochastic Scheduling
• Chapter VII. Bandit Processes
• Appendix: Stochastic Order Relations
• Index