Approximate Dynamic Programming

WARREN B. POWELL, PhD, is Professor of Operations Research and Financial Engineering at Princeton University, where he is founder and Director of CASTLE Laboratory, a research unit that works with industrial partners to test new ideas found in operations research. The recipient of the 2004 INFORMS Fellow Award, Dr. Powell has authored more than 160 published articles on stochastic optimization, approximate dynamicprogramming, and dynamic resource management.

• Preface to the Second Edition xi Preface to the First Edition xvAcknowledgments xvii1 The Challenges of Dynamic Programming 11.1 A Dynamic Programming Example: A Shortest Path Problem, 21.2 The Three Curses of Dimensionality, 31.3 Some Real Applications, 61.4 Problem Classes, 111.5 The Many Dialects of Dynamic Programming, 151.6 What Is New in This Book?, 171.7 Pedagogy, 191.8 Bibliographic Notes, 222 Some Illustrative Models 252.1 Deterministic Problems, 262.2 Stochastic Problems, 312.3 Information Acquisition Problems, 472.4 A Simple Modeling Framework for Dynamic Programs, 502.5 Bibliographic Notes, 54Problems, 543 Introduction to Markov Decision Processes 573.1 The Optimality Equations, 583.2 Finite Horizon Problems, 653.3 Infinite Horizon Problems, 663.4 Value Iteration, 683.5 Policy Iteration, 743.6 Hybrid Value-Policy Iteration, 753.7 Average Reward Dynamic Programming, 763.8 The Linear Programming Method for Dynamic Programs, 773.9 Monotone Policies*, 783.10 Why Does It Work?**, 843.11 Bibliographic Notes, 103Problems, 1034 Introduction to Approximate Dynamic Programming 1114.1 The Three Curses of Dimensionality (Revisited), 1124.2 The Basic Idea, 1144.3 Q-Learning and SARSA, 1224.4 Real-Time Dynamic Programming, 1264.5 Approximate Value Iteration, 1274.6 The Post-Decision State Variable, 1294.7 Low-Dimensional Representations of Value Functions, 1444.8 So Just What Is Approximate Dynamic Programming?, 1464.9 Experimental Issues, 1494.10 But Does It Work?, 1554.11 Bibliographic Notes, 156Problems, 1585 Modeling Dynamic Programs 1675.1 Notational Style, 1695.2 Modeling Time, 1705.3 Modeling Resources, 1745.4 The States of Our System, 1785.5 Modeling Decisions, 1875.6 The Exogenous Information Process, 1895.7 The Transition Function, 1985.8 The Objective Function, 2065.9 A Measure-Theoretic View of Information**, 2115.10 Bibliographic Notes, 213Problems, 2146 Policies 2216.1 Myopic Policies, 2246.2 Lookahead Policies, 2246.3 Policy Function Approximations, 2326.4 Value Function Approximations, 2356.5 Hybrid Strategies, 2396.6 Randomized Policies, 2426.7 How to Choose a Policy?, 2446.8 Bibliographic Notes, 247Problems, 2477 Policy Search 2497.1 Background, 2507.2 Gradient Search, 2537.3 Direct Policy Search for Finite Alternatives, 2567.4 The Knowledge Gradient Algorithm for Discrete Alternatives, 2627.5 Simulation Optimization, 2707.6 Why Does It Work?**, 2747.7 Bibliographic Notes, 285Problems, 2868 Approximating Value Functions 2898.1 Lookup Tables and Aggregation, 2908.2 Parametric Models, 3048.3 Regression Variations, 3148.4 Nonparametric Models, 3168.5 Approximations and the Curse of Dimensionality, 3258.6 Why Does It Work?**, 3288.7 Bibliographic Notes, 333Problems, 3349 Learning Value Function Approximations 3379.1 Sampling the Value of a Policy, 3379.2 Stochastic Approximation Methods, 3479.3 Recursive Least Squares for Linear Models, 3499.4 Temporal Difference Learning with a Linear Model, 3569.5 Bellman’s Equation Using a Linear Model, 3589.6 Analysis of TD(0), LSTD, and LSPE Using a Single State, 3649.7 Gradient-Based Methods for Approximate Value Iteration*, 3669.8 Least Squares Temporal Differencing with Kernel Regression*, 3719.9 Value Function Approximations Based on Bayesian Learning*, 3739.10 Why Does It Work*, 3769.11 Bibliographic Notes, 379Problems, 38110 Optimizing While Learning 38310.1 Overview of Algorithmic Strategies, 38510.2 Approximate Value Iteration and Q-Learning Using Lookup Tables, 38610.3 Statistical Bias in the Max Operator, 39710.4 Approximate Value Iteration and Q-Learning Using Linear Models, 40010.5 Approximate Policy Iteration, 40210.6 The Actor–Critic Paradigm, 40810.7 Policy Gradient Methods, 41010.8 The Linear Programming Method Using Basis Functions, 41110.9 Approximate Policy Iteration Using Kernel Regression*, 41310.10 Finite Horizon Approximations for Steady-State Applications, 41510.11 Bibliographic Notes, 416Problems, 41811 Adaptive Estimation and Stepsizes 41911.1 Learning Algorithms and Stepsizes, 42011.2 Deterministic Stepsize Recipes, 42511.3 Stochastic Stepsizes, 43311.4 Optimal Stepsizes for Nonstationary Time Series, 43711.5 Optimal Stepsizes for Approximate Value Iteration, 44711.6 Convergence, 44911.7 Guidelines for Choosing Stepsize Formulas, 45111.8 Bibliographic Notes, 452Problems, 45312 Exploration Versus Exploitation 45712.1 A Learning Exercise: The Nomadic Trucker, 45712.2 An Introduction to Learning, 46012.3 Heuristic Learning Policies, 46412.4 Gittins Indexes for Online Learning, 47012.5 The Knowledge Gradient Policy, 47712.6 Learning with a Physical State, 48212.7 Bibliographic Notes, 492Problems, 49313 Value Function Approximations for Resource Allocation Problems 49713.1 Value Functions versus Gradients, 49813.2 Linear Approximations, 49913.3 Piecewise-Linear Approximations, 50113.4 Solving a Resource Allocation Problem Using Piecewise-Linear Functions, 50513.5 The SHAPE Algorithm, 50913.6 Regression Methods, 51313.7 Cutting Planes*, 51613.8 Why Does It Work?**, 52813.9 Bibliographic Notes, 535Problems, 53614 Dynamic Resource Allocation Problems 54114.1 An Asset Acquisition Problem, 54114.2 The Blood Management Problem, 54714.3 A Portfolio Optimization Problem, 55714.4 A General Resource Allocation Problem, 56014.5 A Fleet Management Problem, 57314.6 A Driver Management Problem, 58014.7 Bibliographic Notes, 585Problems, 58615 Implementation Challenges 59315.1 Will ADP Work for Your Problem?, 59315.2 Designing an ADP Algorithm for Complex Problems, 59415.3 Debugging an ADP Algorithm, 59615.4 Practical Issues, 59715.5 Modeling Your Problem, 60215.6 Online versus Offline Models, 60415.7 If It Works, Patent It!, 606Bibliography 607Index 623