#### Overview of this book

Reinforcement learning (RL) is a branch of machine learning that has gained popularity in recent times. It allows you to train AI models that learn from their own actions and optimize their behavior. PyTorch has also emerged as the preferred tool for training RL models because of its efficiency and ease of use. With this book, you'll explore the important RL concepts and the implementation of algorithms in PyTorch 1.x. The recipes in the book, along with real-world examples, will help you master various RL techniques, such as dynamic programming, Monte Carlo simulations, temporal difference, and Q-learning. You'll also gain insights into industry-specific applications of these techniques. Later chapters will guide you through solving problems such as the multi-armed bandit problem and the cartpole problem using the multi-armed bandit algorithm and function approximation. You'll also learn how to use Deep Q-Networks to complete Atari games, along with how to effectively implement policy gradients. Finally, you'll discover how RL techniques are applied to Blackjack, Gridworld environments, internet advertising, and the Flappy Bird game. By the end of this book, you'll have developed the skills you need to implement popular RL algorithms and use RL techniques to solve real-world problems.
Table of Contents (11 chapters)
Preface
Free Chapter
Getting Started with Reinforcement Learning and PyTorch
Markov Decision Processes and Dynamic Programming
Monte Carlo Methods for Making Numerical Estimations
Capstone Project – Playing Flappy Bird with DQN
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# Developing Q-learning with linear function approximation

In the previous recipe, we developed a value estimator based on linear regression. We will employ the estimator in Q-learning, as part of our FA journey.

As we have seen, Q-learning is an off-policy learning algorithm and it updates the Q-function based on the following equation:

Here, s' is the resulting state after taking action, a, in state, s; r is the associated reward; α is the learning rate; and γ is the discount factor. Also, means that the behavior policy is greedy, where the highest Q-value among those in state s' is selected to generate learning data. In Q-learning, actions are taken on the basis of the epsilon-greedy policy. Similarly, Q-learning with FA has the following error term:

Our learning goal is to minimize the error term to zero, which means the estimated V(st) should satisfy...