Introduction to Stochastic Dynamic Programming

【实例简介】
“Introduction to Stochastic Dynamic Programming”介绍了 随机动态规划的理论、应用、方法论等一系列。本书由学术泰斗 Sheldon Ross 编写，是学习 随机动态规划的极佳教材。 另外，本书的扫描质量很高，已经经过 OCR， 支持文本搜索
CoPYRIGHT 1983, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS. ELECTRONIC OR MECHANICAL. INCLUDING PHOTOCOPY RECORDING. OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER ACADEMIC PRESS, INC. 111 Fifth Avenue, New York, New York 10003 United Kingdom Edition published b ACADEMIC PRESS, INC. (LONDON) LTD 24/28 Oval Road, London Nw1 7DX Library of Congress Cataloging in Publication Data Ross. She l don M Int roduct ion to stochast ic dynamic programming (Probab i l ity and mathematical statistics) Includes bibl iographies and index ynamic prog Stochastic progr amming i. series T57.83R671982 519.7103 82-18163 SBN0-12-598420-0 PRINTED IN THE UNITED STATES OF AMERICA 83848586 87654321 To Celine Contents L. Finite-Stage Models 1. Introduction 2. A Gambling Model 2 3. A Stock-Option model 4. Modular Functions and monotone policies 5 5. Accepting the Best Offer 6. A Sequential Allocation Model 7. The Interchange Argument in Sequencing 17 Problems 21 Notes and References 26 ll Discounted Dynamic Programming Introduction 29 2. The Optimality Equation and Optimal Policy 3. Method of Successive Approximations 4. Policy Improvement 38 5. Solution by Linear Programming 40 6. Extension to Unbounded Rewards 42 Problems 44 Refe Ill. Minimizing Costs-Negative Dynamic Programming 1. Introduction and Some Theoretical results 2. Optimal Stopping Problems 51 CoNTENTS 3. Bayesian Sequential Analysis 4. Computational approaches 5. Optimal search Problems References 71 I. Maximizing Rewards--Positive Dynamic Programming 1. Introduction and main Theoretical results 2. Applications to Gambling Theory 76 3. Computational Approaches to Obtaining V 83 Problems 85 Notes and references 88 V. Average Reward Criterion 1. Introduction and Counterexamples 2. Existence of an Optimal Stationary Policy 3. Computational Approaches 98 Problems 103 Notes and References 105 VI. Stochastic Scheduling 107 2. Maximizing Finite-Time Returns-Single Processor 108 3. Minimizing Expected Makespan-Processors in Paralle 4. Minimizing Expected Makespan-Processors in Series 114 5. Maximizing Total Field Life 118 6. A Stochastic Knapsack Model 122 7. A Sequential-Assignment Problem 124 Problems 127 Notes and references 129 Vl. Bandit Processes 131 2. Single-Project Bandit Processes 131 3. Multiproject Bandit Processes 133 4. An Extension and a nonextension 5. Generalizations of the classical bandit problem 145 Problems Notes and references 151 CONTENTS Appendix: Stochastic Order Relations 1. Stochastically Larger l53 2. Coupling 154 3. Hazard-Rate Ordering l56 4. Likelihood-Ratio Ordering l57 Problems 160 Reference 161 Index 163 Preface This text presents the basic theory and examines the scope of applications of stochastic dynamic programming. Chapter I is a study of a variety of finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Later chapters study infinite-stage models: dis counting future returns in Chapter Il, minimizing nonnegative costs in Chapter Ill, maximizing nonnegative returns in Chapter IV, and maximiz ing the long-run average return in Chapter V. Each of these chapters first considers whether an optimal policy need exist--presenting counterexam- ples where appropriate-and then presents methods for obtaining such policies when they do. In addition, general areas of application are pre sented; for example, optimal stopping problems are considered in Chapter I and a variety of gambling models in Chapter Iv. The final two chapters are concerned with more specialized models. Chapter vi presents a variety of stochastic scheduling models, and Chapter VII examines 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 expecta tion-is necessary. I have attempted to present all proofs in as intuitive a manner as possible. An appendix dealing with stochastic order relations which is needed primarily for the final two chapters, is included Through- out the text I use the terms increasing and nondecreasing interchangeably 【实例截图】
【核心代码】