Reinforcement Learning, Second Edition

An Introduction

by Sutton, Barto

| ISBN: 9780262352697 | Copyright 0

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The significantly expanded and updated new edition of a widely used text on reinforcement learning, one of the most active research areas in artificial intelligence.

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 while interacting with a complex, uncertain environment. In Reinforcement Learning, Richard Sutton and Andrew Barto provide a clear and simple account of the field's key ideas and algorithms. This second edition has been significantly expanded and updated, presenting new topics and updating coverage of other topics.

Like the first edition, this second edition focuses on core online learning algorithms, with the more mathematical material set off in shaded boxes. Part I covers as much of reinforcement learning as possible without going beyond the tabular case for which exact solutions can be found. Many algorithms presented in this part are new to the second edition, including UCB, Expected Sarsa, and Double Learning. Part II extends these ideas to function approximation, with new sections on such topics as artificial neural networks and the Fourier basis, and offers expanded treatment of off-policy learning and policy-gradient methods. Part III has new chapters on reinforcement learning's relationships to psychology and neuroscience, as well as an updated case-studies chapter including AlphaGo and AlphaGo Zero, Atari game playing, and IBM Watson's wagering strategy. The final chapter discusses the future societal impacts of reinforcement learning.

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Contents (pg. vii)
Preface to the Second Edition (pg. xiii)
Preface to the First Edition (pg. xvii)
Summary of Notation (pg. xix)
1. Introduction (pg. 1)
1.1 Reinforcement Learning (pg. 1)
1.2 Examples (pg. 4)
1.3 Elements of Reinforcement Learning (pg. 6)
1.4 Limitations and Scope (pg. 7)
1.5 An Extended Example: Tic-Tac-Toe (pg. 8)
1.6 Summary (pg. 13)
1.7 Early History of Reinforcement Learning (pg. 13)
I. Tabular Solution Methods (pg. 23)
2. Multi-armed Bandits (pg. 25)
2.1 A k-armed Bandit Problem (pg. 25)
2.2 Action-value Methods (pg. 27)
2.3 The 10-armed Testbed (pg. 28)
2.4 Incremental Implementation (pg. 30)
2.5 Tracking a Nonstationary Problem (pg. 32)
2.6 Optimistic Initial Values (pg. 34)
2.7 Upper-Confidence-Bound Action Selection (pg. 35)
2.8 Gradient Bandit Algorithms (pg. 37)
2.9 Associative Search (Contextual Bandits) (pg. 41)
2.10 Summary (pg. 42)
3. Finite Markov Decision Processes (pg. 47)
3.1 The Agent–Environment Interface (pg. 47)
3.2 Goals and Rewards (pg. 53)
3.3 Returns and Episodes (pg. 54)
3.4 Unified Notation for Episodic and Continuing Tasks (pg. 57)
3.5 Policies and Value Functions (pg. 58)
3.6 Optimal Policies and Optimal Value Functions (pg. 62)
3.7 Optimality and Approximation (pg. 67)
3.8 Summary (pg. 68)
4. Dynamic Programming (pg. 73)
4.1 Policy Evaluation (Prediction) (pg. 74)
4.2 Policy Improvement (pg. 76)
4.3 Policy Iteration (pg. 80)
4.4 Value Iteration (pg. 82)
4.5 Asynchronous Dynamic Programming (pg. 85)
4.6 Generalized Policy Iteration (pg. 86)
4.7 Efficiency of Dynamic Programming (pg. 87)
4.8 Summary (pg. 88)
5. Monte Carlo Methods (pg. 91)
5.1 Monte Carlo Prediction (pg. 92)
5.2 Monte Carlo Estimation of Action Values (pg. 96)
5.3 Monte Carlo Control (pg. 97)
5.4 Monte Carlo Control without Exploring Starts (pg. 100)
5.5 Off-policy Prediction via Importance Sampling (pg. 103)
5.6 Incremental Implementation (pg. 109)
5.7 Off-policy Monte Carlo Control (pg. 110)
5.8 *Discounting-aware Importance Sampling (pg. 112)
5.9 *Per-decision Importance Sampling (pg. 114)
5.10 Summary (pg. 115)
6. Temporal-Difference Learning (pg. 119)
6.1 TD Prediction (pg. 119)
6.2 Advantages of TD Prediction Methods (pg. 124)
6.3 Optimality of TD(0) (pg. 126)
6.4 Sarsa: On-policy TD Control (pg. 129)
6.5 Q-learning: Off-policy TD Control (pg. 131)
6.6 Expected Sarsa (pg. 133)
6.7 Maximization Bias and Double Learning (pg. 134)
6.8 Games, Afterstates, and Other Special Cases (pg. 136)
6.9 Summary (pg. 138)
7. n-step Bootstrapping (pg. 141)
7.1 n-step TD Prediction (pg. 142)
7.2 n-step Sarsa (pg. 145)
7.3 n-step Off-policy Learning (pg. 148)
7.4 *Per-decision Methods with Control Variates (pg. 150)
7.5 Off-policy Learning Without Importance Sampling: The n-step Tree Backup Algorithm (pg. 152)
7.6 *A Unifying Algorithm: n-step Q(σ) (pg. 154)
7.7 Summary (pg. 157)
8. Planning and Learning with Tabular Methods (pg. 159)
8.1 Models and Planning (pg. 159)
8.2 Dyna: Integrated Planning, Acting, and Learning (pg. 161)
8.3 When the Model Is Wrong (pg. 166)
8.4 Prioritized Sweeping (pg. 168)
8.5 Expected vs. Sample Updates (pg. 172)
8.6 Trajectory Sampling (pg. 174)
8.7 Real-time Dynamic Programming (pg. 177)
8.8 Planning at Decision Time (pg. 180)
8.9 Heuristic Search (pg. 181)
8.10 Rollout Algorithms (pg. 183)
8.11 Monte Carlo Tree Search (pg. 185)
8.12 Summary of the Chapter (pg. 188)
8.13 Summary of Part I: Dimensions (pg. 189)
II. Approximate Solution Methods (pg. 195)
9. On-policy Prediction with Approximation (pg. 197)
9.1 Value-function Approximation (pg. 198)
9.2 The Prediction Objective (VE) (pg. 199)
9.3 Stochastic-gradient and Semi-gradient Methods (pg. 200)
9.4 Linear Methods (pg. 204)
9.5 Feature Construction for Linear Methods (pg. 210)
9.6 Selecting Step-Size Parameters Manually (pg. 222)
9.7 Nonlinear Function Approximation: Artificial Neural Networks (pg. 223)
9.8 Least-Squares TD (pg. 228)
9.9 Memory-based Function Approximation (pg. 230)
9.10 Kernel-based Function Approximation (pg. 232)
9.11 Looking Deeper at On-policy Learning: Interest and Emphasis (pg. 234)
9.12 Summary (pg. 236)
10. On-policy Control with Approximation (pg. 243)
10.1 Episodic Semi-gradient Control (pg. 243)
10.2 Semi-gradient n-step Sarsa (pg. 247)
10.3 Average Reward: A New Problem Setting for Continuing Tasks (pg. 249)
10.4 Deprecating the Discounted Setting (pg. 253)
10.5 Differential Semi-gradient n-step Sarsa (pg. 255)
10.6 Summary (pg. 256)
11. *Off-policy Methods with Approximation (pg. 257)
11.1 Semi-gradient Methods (pg. 258)
11.2 Examples of Off-policy Divergence (pg. 260)
11.3 The Deadly Triad (pg. 264)
11.4 Linear Value-function Geometry (pg. 266)
11.5 Gradient Descent in the Bellman Error (pg. 269)
11.6 The Bellman Error is Not Learnable (pg. 274)
11.7 Gradient-TD Methods (pg. 278)
11.8 Emphatic-TD Methods (pg. 281)
11.9 Reducing Variance (pg. 283)
11.10 Summary (pg. 284)
12. Eligibility Traces (pg. 287)
12.1 The λ-return (pg. 288)
12.2 TD(λ) (pg. 292)
12.3 n-step Truncated λ-return Methods (pg. 295)
12.4 Redoing Updates: Online λ-return Algorithm (pg. 297)
12.5 True Online TD(λ) (pg. 299)
12.6 *Dutch Traces in Monte Carlo Learning (pg. 301)
12.7 Sarsa(λ) (pg. 303)
12.8 Variable λ and γ (pg. 307)
12.9 Off-policy Traces with Control Variates (pg. 309)
12.10 Watkins's Q(λ) to Tree-Backup(λ) (pg. 312)
12.11 Stable Off-policy Methods with Traces (pg. 314)
12.12 Implementation Issues (pg. 316)
12.13 Conclusions (pg. 317)
13. Policy Gradient Methods (pg. 321)
13.1 Policy Approximation and its Advantages (pg. 322)
13.2 The Policy Gradient Theorem (pg. 324)
13.3 REINFORCE: Monte Carlo Policy Gradient (pg. 326)
13.4 REINFORCE with Baseline (pg. 329)
13.5 Actor–Critic Methods (pg. 331)
13.6 Policy Gradient for Continuing Problems (pg. 333)
13.7 Policy Parameterization for Continuous Actions (pg. 335)
13.8 Summary (pg. 337)
III. Looking Deeper (pg. 339)
14. Psychology (pg. 341)
14.1 Prediction and Control (pg. 342)
14.2 Classical Conditioning (pg. 343)
14.3 Instrumental Conditioning (pg. 357)
14.4 Delayed Reinforcement (pg. 361)
14.5 Cognitive Maps (pg. 363)
14.6 Habitual and Goal-directed Behavior (pg. 364)
14.7 Summary (pg. 368)
15. Neuroscience (pg. 377)
15.1 Neuroscience Basics (pg. 378)
15.2 Reward Signals, Reinforcement Signals, Values, and Prediction Errors (pg. 380)
15.3 The Reward Prediction Error Hypothesis (pg. 381)
15.4 Dopamine (pg. 383)
15.5 Experimental Support for the Reward Prediction Error Hypothesis (pg. 387)
15.6 TD Error/Dopamine Correspondence (pg. 390)
15.7 Neural Actor–Critic (pg. 395)
15.8 Actor and Critic Learning Rules (pg. 398)
15.9 Hedonistic Neurons (pg. 402)
15.10 Collective Reinforcement Learning (pg. 404)
15.11 Model-based Methods in the Brain (pg. 407)
15.12 Addiction (pg. 409)
15.13 Summary (pg. 410)
16. Applications and Case Studies (pg. 421)
16.1 TD-Gammon (pg. 421)
16.2 Samuel's Checkers Player (pg. 426)
16.3 Watson's Daily-Double Wagering (pg. 429)
16.4 Optimizing Memory Control (pg. 432)
16.5 Human-level Video Game Play (pg. 436)
16.6 Mastering the Game of Go (pg. 441)
16.7 Personalized Web Services (pg. 450)
16.8 Thermal Soaring (pg. 453)
17. Frontiers (pg. 459)
17.1 General Value Functions and Auxiliary Tasks (pg. 459)
17.2 Temporal Abstraction via Options (pg. 461)
17.3 Observations and State (pg. 464)
17.4 Designing Reward Signals (pg. 469)
17.5 Remaining Issues (pg. 472)
17.6 Experimental Support for the Reward Prediction Error Hypothesis (pg. 475)
References (pg. 481)
Index (pg. 481)

Richard S. Sutton

Richard S. Sutton is Professor of Computing Science and AITF Chair in Reinforcement Learning and Artificial Intelligence at the University of Alberta, and also Distinguished Research Scientist at DeepMind.

Andrew G. Barto

Andrew G. Barto is Professor Emeritus in the College of Computer and Information Sciences at the University of Massachusetts Amherst.

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