Here are 100 chapter titles for a book on Reinforcement Learning (RL), progressing from beginner to advanced, with a focus on the mathematical aspects:
I. Foundations and Core Concepts (20 Chapters)
- Introduction to Reinforcement Learning: What and Why?
- Markov Decision Processes (MDPs): Formal Definition
- States, Actions, Rewards, and Policies
- The Goal of Reinforcement Learning: Maximizing Cumulative Reward
- Episodic vs. Continuing Tasks
- Discounting and Discounted Rewards
- The Bellman Equation: The Heart of RL
- Value Functions: State Values and Action Values
- Optimal Policies and Optimal Value Functions
- Dynamic Programming for Solving MDPs: Policy Iteration
- Dynamic Programming for Solving MDPs: Value Iteration
- Introduction to Model-Free RL
- Monte Carlo Methods: Estimating Value Functions
- Temporal Difference Learning: TD(0) and TD(1)
- SARSA: On-Policy TD Control
- Q-Learning: Off-Policy TD Control
- Exploration-Exploitation Dilemma: ε-greedy, Softmax
- Function Approximation: Linear Methods
- Function Approximation: Non-linear Methods (Neural Networks)
- Basic RL Algorithms: A Summary
II. Advanced RL Algorithms and Techniques (30 Chapters)
- Eligibility Traces: Generalizing TD Learning
- TD(λ): Combining Monte Carlo and TD
- SARSA(λ) and Q(λ)
- Planning with Learned Models: Model-Based RL
- Dyna-Q: Integrating Planning and Learning
- Prioritized Sweeping
- Approximate Dynamic Programming
- Least-Squares Policy Iteration (LSPI)
- Policy Gradient Methods: REINFORCE
- Policy Gradient Methods: Actor-Critic
- Deterministic Policy Gradients
- Natural Policy Gradients
- Trust Region Policy Optimization (TRPO)
- Proximal Policy Optimization (PPO)
- Deep Reinforcement Learning: Introduction
- Deep Q-Networks (DQN)
- Double DQN and Dueling DQN
- Prioritized Experience Replay
- Deep Deterministic Policy Gradients (DDPG)
- Continuous Action Spaces
- Partially Observable Markov Decision Processes (POMDPs)
- Belief States and POMDPs
- Solving POMDPs: Algorithms and Approximations
- Multi-Agent Reinforcement Learning (MARL)
- Game Theory and Multi-Agent Systems
- Cooperative and Competitive MARL
- Communication in Multi-Agent Systems
- Distributed Reinforcement Learning
- Hierarchical Reinforcement Learning
- Options and Hierarchical Policies
III. Theoretical Foundations and Analysis (30 Chapters)
- Convergence Analysis of TD Learning
- Convergence Analysis of Q-Learning
- Convergence Analysis of Policy Gradient Methods
- Sample Complexity in Reinforcement Learning
- Regret Bounds and Optimality
- Concentration Inequalities and their use in RL
- Stochastic Approximation Theory
- Lyapunov Functions and Stability Analysis
- Banach Contraction Mapping Theorem and its Applications
- Bellman Equations in Banach Spaces
- Function Approximation Theory
- Reproducing Kernel Hilbert Spaces (RKHS) and RL
- Kernel Methods in Reinforcement Learning
- Non-parametric Reinforcement Learning
- Bayesian Reinforcement Learning
- Gaussian Processes in RL
- Information-Theoretic Approaches to RL
- Reinforcement Learning and Optimal Control
- Linear Quadratic Regulator (LQR) and RL
- H-infinity Control and Robust RL
- Connections to other areas of mathematics (e.g., probability, optimization)
- Reinforcement Learning and Dynamical Systems
- Reinforcement Learning and Stochastic Processes
- Reinforcement Learning and Game Theory: Advanced topics
- Mean Field Reinforcement Learning
- Multi-armed bandits: Advanced topics and connections to RL
- Contextual bandits
- Imitation Learning: Introduction
- Inverse Reinforcement Learning
- Generative Adversarial Imitation Learning (GAIL)
IV. Advanced Topics and Applications (20 Chapters)
- Reinforcement Learning for Robotics
- Reinforcement Learning for Control Systems
- Reinforcement Learning for Natural Language Processing
- Reinforcement Learning for Computer Vision
- Reinforcement Learning for Recommender Systems
- Reinforcement Learning for Games
- Reinforcement Learning for Healthcare
- Reinforcement Learning for Finance
- Reinforcement Learning for Resource Management
- Reinforcement Learning for Combinatorial Optimization
- Transfer Learning in Reinforcement Learning
- Meta-Learning for Reinforcement Learning
- Curriculum Learning in Reinforcement Learning
- Safe Reinforcement Learning
- Explainable Reinforcement Learning
- The Future of Reinforcement Learning
- Ethical Considerations in Reinforcement Learning
- Software and Tools for Reinforcement Learning
- Open Problems in Reinforcement Learning
- Appendix: Foundational Material and References