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Introduction to Stochastic Dynamic Programming

1st Edition - March 28, 1983

Author: Sheldon M. Ross

Editors: Z. W. Birnbaum, E. Lukacs

eBook ISBN:

9 7 8 - 1 - 4 8 3 2 - 6 9 0 9 - 2

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… Read more

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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.

PrefaceI. 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 ReferencesII. 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 ReferencesIII. 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 ReferencesIV. 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 ReferencesV. Average Reward Criterion 1. Introduction and Counterexamples 2. Existence of an Optimal Stationary Policy 3. Computational Approaches Problems Notes and ReferencesVI. 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 ReferencesVII. 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 ReferencesAppendix: Stochastic Order Relations 1. Stochastically Larger 2. Coupling 3. Hazard-Rate Ordering 4. Likelihood-Ratio Ordering Problems ReferenceIndex