Understanding approximate dynamic programming (ADP) in large industrial settings helps develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, this second edition of Approximate Dynamic Programming Solving the Curses of Dimensionality uniquely integrates four distinct disciplines Markov design processes, mathematical programming, simulation, and statistics to show students, practitioners, and researchers how to successfully model and solve a wide range of real-life problems using ADP.
Preface to the Second Edition xi Preface to the First Edition xv Acknowledgments xvii 1 The Challenges of Dynamic Programming 1 1.1 A Dynamic Programming Example: A Shortest Path Problem, 2 1.2 The Three Curses of Dimensionality, 3 1.3 Some Real Applications, 6 1.4 Problem Classes, 11 1.5 The Many Dialects of Dynamic Programming, 15 1.6 What Is New in This Book?, 17 1.7 Pedagogy, 19 1.8 Bibliographic Notes, 22 2 Some Illustrative Models 25 2.1 Deterministic Problems, 26 2.2 Stochastic Problems, 31 2.3 Information Acquisition Problems, 47 2.4 A Simple Modeling Framework for Dynamic Programs, 50 2.5 Bibliographic Notes, 54 Problems, 54 3 Introduction to Markov Decision Processes 57 3.1 The Optimality Equations, 58 3.2 Finite Horizon Problems, 65 3.3 Infinite Horizon Problems, 66 3.4 Value Iteration, 68 3.5 Policy Iteration, 74 3.6 Hybrid Value-Policy Iteration, 75 3.7 Average Reward Dynamic Programming, 76 3.8 The Linear Programming Method for Dynamic Programs, 77 3.9 Monotone Policies, 78 3.10 Why Does It Work?, 84 3.11 Bibliographic Notes, 103 Problems, 103 4 Introduction to Approximate Dynamic Programming 111 4.1 The Three Curses of Dimensionality (Revisited), 112 4.2 The Basic Idea, 114 4.3 Q-Learning and SARSA, 122 4.4 Real-Time Dynamic Programming, 126 4.5 Approximate Value Iteration, 127 4.6 The Post-Decision State Variable, 129 4.7 Low-Dimensional Representations of Value Functions, 144 4.8 So Just What Is Approximate Dynamic Programming?, 146 4.9 Experimental Issues, 149 4.10 But Does It Work?, 155 4.11 Bibliographic Notes, 156 Problems, 158 5 Modeling Dynamic Programs 167 5.1 Notational Style, 169 5.2 Modeling Time, 170 5.3 Modeling Resources, 174 5.4 The States of Our System, 178 5.5 Modeling Decisions, 187 5.6 The Exogenous Information Process, 189 5.7 The Transition Function, 198 5.8 The Objective Function, 206 5.9 A Measure-Theoretic View of Information, 211 5.10 Bibliographic Notes, 213 Problems, 214 6 Policies 221 6.1 Myopic Policies, 224 6.2 Lookahead Policies, 224 6.3 Policy Function Approximations, 232 6.4 Value Function Approximations, 235 6.5 Hybrid Strategies, 239 6.6 Randomized Policies, 242 6.7 How to Choose a Policy?, 244 6.8 Bibliographic Notes, 247 Problems, 247 7 Policy Search 249 7.1 Background, 250 7.2 Gradient Search, 253 7.3 Direct Policy Search for Finite Alternatives, 256 7.4 The Knowledge Gradient Algorithm for Discrete Alternatives, 262 7.5 Simulation Optimization, 270 7.6 Why Does It Work?, 274 7.7 Bibliographic Notes, 285 Problems, 286 8 Approximating Value Functions 289 8.1 Lookup Tables and Aggregation, 290 8.2 Parametric Models, 304 8.3 Regression Variations, 314 8.4 Nonparametric Models, 316 8.5 Approximations and the Curse of Dimensionality, 325 8.6 Why Does It Work?, 328 8.7 Bibliographic Notes, 333 Problems, 334 9 Learning Value Function Approximations 337 9.1 Sampling the Value of a Policy, 337 9.2 Stochastic Approximation Methods, 347 9.3 Recursive Least Squares for Linear Models, 349 9.4 Temporal Difference Learning with a Linear Model, 356 9.5 Bellman's Equation Using a Linear Model, 358 9.6 Analysis of TD(0), LSTD, and LSPE Using a Single State, 364 9.7 Gradient-Based Methods for Approximate Value Iteration, 366 9.8 Least Squares Temporal Differencing with Kernel Regression, 371 9.9 Value Function Approximations Based on Bayesian Learning, 373 9.10 Why Does It Work, 376 9.11 Bibliographic Notes, 379 Problems, 381 10 Optimizing While Learning 383 10.1 Overview of Algorithmic Strategies, 385 10.2 Approximate Value Iteration and Q-Learning Using Lookup Tables, 386 10.3 Statistical Bias in the Max Operator, 397 10.4 Approximate Value Iteration and Q-Learning Using Linear Models, 400 10.5 Approximate Policy Iteration, 402 10.6 The Actor-Critic Paradigm, 408 10.7 Policy Gradient Methods, 410 10.8 The Linear Programming Method Using Basis Functions, 411 10.9 Approximate Policy Iteration Using Kernel Regression, 413 10.10 Finite Horizon Approximations for Steady-State Applications, 415 1
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