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.
Preface I. Finite-Stage Models1. 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 Programming1. 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 Programming1. 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 Programming1. Introduction and Main Theoretical Results 2. Applications to Gambling Theory 3. Computational Approaches to Obtaining V Problems Notes and References
V. Average Reward Criterion1. Introduction and Counterexamples 2. Existence of an Optimal Stationary Policy 3. Computational Approaches Problems Notes and References
VI. Stochastic Scheduling1. 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 Processes1. 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 Relatio
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- © Academic Press 1983
- 28th March 1983
- Academic Press
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Sheldon M. Ross is a professor in the Department of Industrial Engineering and Operations Research at the University of Southern California. He received his Ph.D. 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, and a recipient of the Humboldt US Senior Scientist Award.
University of Southern California, Los Angeles, USA
Bowling Green State University