Overview of this Book
Chapter 1 Basic Concepts
1.1 A grid world example
1.2 State and action
1.3 State transition
1.4 Policy
1.5 Reward
1.6 Trajectories, returns, and episodes
1.7 Markov decision processes
1.8 Summary
1.9 Q&A
Chapter 2 State Values and the Bellman Equation
2.1 Motivating example 1: Why are returns important?
2.2 Motivating example 2: How to calculate returns?
2.3 State values
2.4 The Bellman equation
2.5 Examples for illustrating the Bellman equation
2.6 Matrix-vector form of the Bellman equation
2.7 Solving state values from the Bellman equation
2.7.1 Closed-form solution
2.7.2 Iterative solution
2.7.3 Illustrative examples
2.8 From state value to action value
2.8.1 Illustrative examples
2.8.2 The Bellman equation in terms of action values
2.9 Summary
2.10 Q&A
Chapter 3 Optimal State Values and the Bellman Optimality Equation
3.1 Motivating example: How to improve policies?
3.2 Optimal state values and optimal policies
3.3 The Bellman optimality equation
3.3.1 Maximization of the right-hand side of the BOE
3.3.2 Matrix-vector form of the BOE
3.3.3 Contraction mapping theorem
3.3.4 Contraction property of the right-hand side of the BOE
3.4 Solving an optimal policy from the BOE
3.5 Factors that influence optimal policies
3.6 Summary
3.7 Q&A
Chapter 4 Value Iteration and Policy Iteration
4.1 Value iteration
4.1.1 Elementwise form and implementation
4.1.2 Illustrative examples
4.2 Policy iteration
4.2.1 Algorithm analysis
4.2.2 Elementwise form and implementation
4.2.3 Illustrative examples
4.3 Truncated policy iteration
4.3.1 Comparing value iteration and policy iteration
4.3.2 Truncated policy iteration algorithm
4.4 Summary
4.5 Q&A
Chapter 5 Monte Carlo Methods
5.1 Motivating example: Mean estimation
5.2 MC Basic: The simplest MC-based algorithm
5.2.1 Converting policy iteration to be model-free
5.2.2 The MC Basic algorithm
5.2.3 Illustrative examples
5.3 MC Exploring Starts
5.3.1 Utilizing samples more efficiently
5.3.2 Updating policies more efficiently
5.3.3 Algorithm description
5.4 MC ∈-Greedy: Learning without exploring starts
5.4.1 ∈-greedy policies
5.4.2 Algorithm description
5.4.3 Illustrative examples
5.5 Exploration and exploitation of ∈-greedy policies
5.6 Summary
5.7 Q&A
Chapter 6 Stochastic Approximation
6.1 Motivating example: Mean estimation
6.2 Robbins-Monro algorithm
6.2.1 Convergence properties
6.2.2 Application to mean estimation
6.3 Dvoretzky's convergence theorem
6.3.1 Proof of Dvoretzky's theorem
6.3.2 Application to mean estimation
6.3.3 Application to the Robbins-Monro theorem
6.3.4 An extension of Dvoretzky's theorem
6.4 Stochastic gradient descent
6.4.1 Application to mean estimation
6.4.2 Convergence pattern of SGD
6.4.3 A deterministic formulation of SGD
6.4.4 BGD, SGD, and mini-batch GD
6.4.5 Convergence of SGD
6.5 Summary
6.6 Q&A
Chapter 7 Temporal-Difference Methods
7.1 TD learning of state values
7.1.1 Algorithm description
7.1.2 Property analysis
7.1.3 Convergence analysis
7.2 TD learning of action values: Sarsa
7.2.1 Algorithm description
7.2.2 Optimal policy learning via Sarsa
7.3 TD learning of action values: n-step Sarsa
7.4 TD learning of optimal action values: Q-learning
7.4.1 Algorithm description
7.4.2 Off-policy vs. on-policy
7.4.3 Implementation
7.4.4 Illustrative examples
7.5 A unifed viewpoint
7.6 Summary
7.7 Q&A
Chapter 8 Value Function Approximation
8.1 Value representation: From table to function
8.2 TD learning of state values with function approximation
8.2.1 O
