"本书从强化学习最基本的概念开始介绍, 将介绍基础的分析工具, 包括贝尔曼公式和贝尔曼最
优公式, 然后推广到基于模型的和无模型的强化学习算法, 最后推广到基于函数逼近的强化学习方
法。本书强调从数学的角度引入概念、分析问题、分析算法, 并不强调算法的编程实现。本书不要求
读者具备任何关于强化学习的知识背景, 仅要求读者具备一定的概率论和线性代数的知识。如果读者
已经具备强化学习的学习基础, 本书可以帮助读者更深入地理解一些问题并提供新的视角。
本书面向对强化学习感兴趣的本科生、研究生、研究人员和企业或研究所的从业者。
"

Contents

Overview of this Book\t1
Chapter 1 Basic Concepts \t6
1.1 A grid world example \t7
1.2 State and action\t8
1.3 State transition \t9
1.4 Policy \t11
1.5 Reward\t13
1.6 Trajectories, returns, and episodes \t15
1.7 Markov decision processes\t18
1.8 Summary\t20
1.9 Q&A\t20
Chapter 2 State Values and the Bellman Equation \t21
2.1 Motivating example 1: Why are returns important?\t23
2.2 Motivating example 2: How to calculate returns? \t24
2.3 State values\t26
2.4 The Bellman equation \t27
2.5 Examples for illustrating the Bellman equation \t30
2.6 Matrix-vector form of the Bellman equation\t33
2.7 Solving state values from the Bellman equation\t35
2.7.1 Closed-form solution \t35
2.7.2 Iterative solution\t35
2.7.3 Illustrative examples \t36
2.8 From state value to action value\t38
2.8.1 Illustrative examples \t39
2.8.2 The Bellman equation in terms of action values\t40
2.9 Summary\t41
2.10 Q&A \t42
Chapter 3 Optimal State Values and the Bellman Optimality Equation\t43
3.1 Motivating example: How to improve policies? \t45
3.2 Optimal state values and optimal policies\t46
3.3 The Bellman optimality equation\t47
3.3.1 Maximization of the right-hand side of the BOE \t48
3.3.2 Matrix-vector form of the BOE\t49
3.3.3 Contraction mapping theorem \t50
3.3.4 Contraction property of the right-hand side of the BOE \t53
3.4 Solving an optimal policy from the BOE \t55
3.5 Factors that influence optimal policies\t58
3.6 Summary\t63
3.7 Q&A\t63
Chapter 4 Value Iteration and Policy Iteration\t66
4.1 Value iteration \t68
4.1.1 Elementwise form and implementation \t68
4.1.2 Illustrative examples \t70
4.2 Policy iteration\t72
4.2.1 Algorithm analysis\t73
4.2.2 Elementwise form and implementation \t76
4.2.3 Illustrative examples \t77
4.3 Truncated policy iteration\t81
4.3.1 Comparing value iteration and policy iteration \t81
4.3.2 Truncated policy iteration algorithm \t83
4.4 Summary\t85
4.5 Q&A\t86
Chapter 5 Monte Carlo Methods\t89
5.1 Motivating example: Mean estimation\t91
5.2 MC Basic: The simplest MC-based algorithm\t93
5.2.1 Converting policy iteration to be model-free\t93
5.2.2 The MC Basic algorithm\t94
5.2.3 Illustrative examples \t96
5.3 MC Exploring Starts \t99
5.3.1 Utilizing samples more efficiently \t100
5.3.2 Updating policies more efficiently \t101
5.3.3 Algorithm description\t101
5.4 MC -Greedy: Learning without exploring starts\t102
5.4.1 -greedy policies\t103
5.4.2 Algorithm description\t103
5.4.3 Illustrative examples\t105
5.5 Exploration and exploitation of -greedy policies\t106
5.6 Summary \t111
5.7 Q&A \t111
Chapter 6 Stochastic Approximation\t114
6.1 Motivating example: Mean estimation\t116
6.2 Robbins-Monro algorithm \t117
6.2.1 Convergence properties \t119
6.2.2 Application to mean estimation \t123
6.3 Dvoretzky's convergence theorem \t124
6.3.1 Proof of Dvoretzky's theorem \t125
6.3.2 Application to mean estimation.\t126
6.3.3 Application to the Robbins-Monro theorem \t127
6.3.4 An extension of Dvoretzky's theorem \t127
6.4 Stochastic gradient descent \t128
6.4.1 Application to mean estimation\t130
6.4.2 Convergence pattern of SGD\t131
6.4.3 A deterministic formulation of SGD\t133
6.4.4 BGD, SGD, and mini-batch GD\t134
6.4.5 Convergence of SGD\t136
6.5 Summary \t138
6.6 Q&A \t138
Chapter 7 Temporal-Difference Methods\t140
7.1 TD learning of state values\t142
7.1.1 Algorithm description\t142
7.1.2 Property analysis \t144
7.1.3 Convergence analysis \t146
7.2 TD learning of action values: Sarsa \t149
7.2.1 Algorithm description\t149
7.2.2 Optimal policy learning via Sarsa \t151
7.3 TD learning of action values: n-step Sarsa\t154
7.4 TD learning of optimal action values: Q-learning\t156
7.4.1 Algorithm description\t156
7.4.2 Off-policy vs. on-policy \t158
7.4.3 Implementation\t160
7.4.4 Illustrative examples\t161
7.5 A unified viewpoint \t165
7.6 Summary \t165
7.7 Q&A \t166
Chapter 8 Value Function Approximation\t168
8.1 Value representation: From table to function\t170
8.2 TD learning of state values with function approximation\t174
8.2.1 Objective function\t174
8.2.2 Optimization algorithms\t180
8.2.3 Selection of function approximators \t182
8.2.4 Illustrative examples\t183
8.2.5 Theoretical analysis\t187
8.3 TD learning of action values with function approximation \t198
8.3.1 Sarsa with function approximation\t198
8.3.2 Q-learning with function approximation\t200
8.4 Deep Q-learning\t201
8.4.1 Algorithm description\t202
8.4.2 Illustrative examples\t204
8.5 Summary \t207
8.6 Q&A \t207
Chapter 9 Policy Gradient Methods\t211
9.1 Policy representation: From table to function \t213
9.2 Metrics for defining optimal policies \t214
9.3 Gradients of the metrics\t219
9.3.1 Derivation of the gradients in the discounted case \t221
9.3.2 Derivation of the gradients in the undiscounted case\t226
9.4 Monte Carlo policy gradient (REINFORCE)\t232
9.5 Summary \t235
9.6 Q&A \t235
Chapter 10 Actor-Critic Methods \t237
10.1 The simplest actor-critic algorithm (QAC) \t239
10.2 Advantage actor-critic (A2C)\t240
10.2.1 Baseline invariance\t240
10.2.2 Algorithm description \t243
10.3 Off-policy actor-critic\t244
10.3.1 Importance sampling\t245
10.3.2 The off-policy policy gradient theorem \t247
10.3.3 Algorithm description \t249
10.4 Deterministic actor-critic\t251
10.4.1 The deterministic policy gradient theorem \t251
10.4.2 Algorithm description \t258
10.5 Summary\t259
10.6 Q&A\t260
Appendix A Preliminaries for Probability Theory\t262
Appendix B Measure-Theoretic Probability Theory\t268
Appendix C Convergence of Sequences \t276
C.1 Convergence of deterministic sequences \t277
C.2 Convergence of stochastic sequences\t280
Appendix D Preliminaries for Gradient Descent\t284
Bibliography \t290
Symbols\t297
Index \t299