#### 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.
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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# Calculating Pi using the Monte Carlo method

Let's get started with a simple project: estimating the value of π using the Monte Carlo method, which is the core of model-free reinforcement learning algorithms.

A Monte Carlo method is any method that uses randomness to solve problems. The algorithm repeats suitable random sampling and observes the fraction of samples that obey particular properties in order to make numerical estimations.

Let's do a fun exercise where we approximate the value of π using the MC method. We'll place a large number of random points in a square whose width = 2 (-1<x<1, -1<y<1), and count how many points fall within the circle of unit radius. We all know that the area of the square is:

And the area of the circle is:

If we divide the area of the circle by the area of the square, we have the following:

S/C can be...