#### Overview of this book

Reinforcement Learning (RL) is the trending and most promising branch of artificial intelligence. Hands-On Reinforcement learning with Python will help you master not only the basic reinforcement learning algorithms but also the advanced deep reinforcement learning algorithms. The book starts with an introduction to Reinforcement Learning followed by OpenAI Gym, and TensorFlow. You will then explore various RL algorithms and concepts, such as Markov Decision Process, Monte Carlo methods, and dynamic programming, including value and policy iteration. This example-rich guide will introduce you to deep reinforcement learning algorithms, such as Dueling DQN, DRQN, A3C, PPO, and TRPO. You will also learn about imagination-augmented agents, learning from human preference, DQfD, HER, and many more of the recent advancements in reinforcement learning. By the end of the book, you will have all the knowledge and experience needed to implement reinforcement learning and deep reinforcement learning in your projects, and you will be all set to enter the world of artificial intelligence.
Preface
Free Chapter
Introduction to Reinforcement Learning
Getting Started with OpenAI and TensorFlow
The Markov Decision Process and Dynamic Programming
Gaming with Monte Carlo Methods
Temporal Difference Learning
Multi-Armed Bandit Problem
Deep Learning Fundamentals
Atari Games with Deep Q Network
Playing Doom with a Deep Recurrent Q Network
The Asynchronous Advantage Actor Critic Network
Policy Gradients and Optimization
Capstone Project – Car Racing Using DQN
Recent Advancements and Next Steps
Assessments
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# The Bellman equation and optimality

The Bellman equation, named after Richard Bellman, American mathematician, helps us to solve MDP. It is omnipresent in RL. When we say solve the MDP, it actually means finding the optimal policies and value functions. There can be many different value functions according to different policies. The optimal value function is the one which yields maximum value compared to all the other value functions:

Similarly, the optimal policy is the one which results in an optimal value function.

Since the optimal value function is the one that has a higher value compared to all other value functions (that is, maximum return), it will be the maximum of the Q function. So, the optimal value function can easily be computed by taking the maximum of the Q function as follows:

-- (3)

The Bellman equation for the value function can be represented as, (we...