Introduction to Stochastic Dynamic Programming (PROBABILITY AND MATHEMATICAL STATISTICS)

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. Content: Front Matter, Page iii Copyright, Page iv Dedication, Page v Preface, Page xi I - Finite-Stage Models, Pages 1-27 II - Discounted Dynamic Programming, Pages 29-48 III - Minimizing Costs—Negative Dynamic Programming, Pages 49-71 IV - Maximizing Rewards—Positive Dynamic Programming, Pages 73-88 V - Average Reward Criterion, Pages 89-106 VI - Stochastic Scheduling, Pages 107-130 VII - Bandit Processes, Pages 131-151 Appendix - Stochastic Order Relations, Pages 153-161 Index, Pages 163-164 Probability and Mathematical Statistics: A Series of Monographs and Textbooks, Pages ibc1-ibc2 Sheldon Ross. Includes Bibliographies And Index.