Reinforcement Learning

Richard S. Sutton, Andrew G. Barto





Reinforcement learning, one of the most active research areas in artificial intelligence, is a computational approach to learning whereby an agent tries to maximize the total amount of reward it receives when interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the key ideas and algorithms of reinforcement learning. Their discussion ranges from the history of the field's intellectual foundations to the most recent developments and applications. The only necessary mathematical background is familiarity with elementary concepts of probability.

The book is divided into three parts. Part I defines the reinforcement learning problem in terms of Markov decision processes. Part II provides basic solution methods: dynamic programming, Monte Carlo methods, and temporal-difference learning. Part III presents a unified view of the solution methods and incorporates artificial neural networks, eligibility traces, and planning; the two final chapters present case studies and consider the future of reinforcement learning.

Table of Contents


1 Introduction  
       1.1 Reinforcement Learning  
       1.2 Examples  
       1.3 Elements of Reinforcement Learning  
       1.4 An Extended Example: Tic-Tac-Toe  
       1.5 Summary  
       1.6 History of Reinforcement Learning  
       1.7 Bibliographical Remarks  
2 Evaluative Feedback  
       2.1 An n-Armed Bandit Problem  
       2.2 Action-Value Methods  
       2.3 Softmax Action Selection  
       2.4 Evaluation Versus Instruction  
       2.5 Incremental Implementation  
       2.6 Tracking a Nonstationary Problem  
       2.7 Optimistic Initial Values  
       2.8 Reinforcement Comparison  
       2.9 Pursuit Methods  
       2.10 Associative Search  
       2.11 Conclusions  
       2.12 Bibliographical and Historical Remarks  
3 The Reinforcement Learning Problem  
       3.1 The Agent-Environment Interface  
       3.2 Goals and Rewards  
       3.3 Returns  
       3.4 Unified Notation for Episodic and Continuing Tasks  
       3.5 The Markov Property  
       3.6 Markov Decision Processes  
       3.7 Value Functions  
       3.8 Optimal Value Functions  
       3.9 Optimality and Approximation  
       3.10 Summary  
       3.11 Bibliographical and Historical Remarks  
4 Dynamic Programming  
       4.1 Policy Evaluation  
       4.2 Policy Improvement  
       4.3 Policy Iteration  
       4.4 Value Iteration  
       4.5 Asynchronous Dynamic Programming  
       4.6 Generalized Policy Iteration  
       4.7 Efficiency of Dynamic Programming  
       4.8 Summary  
       4.9 Bibliographical and Historical Remarks  
5 Monte Carlo Methods  
       5.1 Monte Carlo Policy Evaluation  
       5.2 Monte Carlo Estimation of Action Values  
       5.3 Monte Carlo Control  
       5.4 On-Policy Monte Carlo Control  
       5.5 Evaluating One Policy While Following Another  
       5.6 Off-Policy Monte Carlo Control  
       5.7 Incremental Implementation  
       5.8 Summary  
       5.9 Bibliographical and Historical Remarks  
6 Temporal-Difference Learning  
       6.1 TD Prediction  
       6.2 Advantages of TD Prediction Methods  
       6.3 Optimality of TD(O)  
       6.4 Sarsa: On-Policy TD Control  
       6.5 Q-Learning: Off-Policy TD Control  
       6.6 Actor-Critic Methods  
       6.7 R-Learning for Undiscounted Continuing Tasks  
       6.8 Games, Afterstates, and Other Special Cases  
       6.9 Summary  
       6.10 Bibliographical and Historical Remarks  
7 Eligibility Traces  
       7.1 n-Step TD Prediction  
       7.2 The Forward View of TD(l)  
       7.3 The Backward View of TD(l)  
       7.4 Equivalence of Forward and Backward Views  
       7.5 Sarsa(l)  
       7.6 Q(l)  
       7.7 Eligibility Traces for Actor-Critic Methods  
       7.8 Replacing Traces  
       7.9 Implementation Issues  
       7.10 Variable l  
       7.11 Conclusions  
       7.12 Bibliographical and Historical Remarks  
8 Generalization and Function Approximation  
       8.1 Value Prediction with Function Approximation  
       8.2 Gradient-Descent Methods  
       8.3 Linear Methods  
       8.4 Control with Function Approximation  
       8.5 Off-Policy Bootstrapping  
       8.6 Should We Bootstrap?  
       8.7 Summary  
       8.8 Bibliographical and Historical Remarks  
9 Planning and Learning  
       9.1 Models and Planning  
       9.2 Integrating Planning, Acting, and Learning  
       9.3 When the Model Is Wrong  
       9.4 Prioritized Sweeping  
       9.5 Full vs. Sample Backups  
       9.6 Trajectory Sampling  
       9.7 Heuristic Search  
       9.8 Summary  
       9.9 Bibliographical and Historical Remarks  
10 Dimensions of Reinforcement Learning  
       10.1 The Unified View  
       10.2 Other Frontier Dimensions  
11 Case Studies  
       11.1 TD-Gammon  
       11.2 Samuel's Checkers Player  
       11.3 The Acrobot  
       11.4 Elevator Dispatching  
       11.5 Dynamic Channel Allocation  
       11.6 Job-Shop Scheduling