#### 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
Other Books You May Enjoy

# Solving an MDP with a value iteration algorithm

An MDP is considered solved if its optimal policy is found. In this recipe, we will figure out the optimal policy for the FrozenLake environment using a value iteration algorithm.

The idea behind value iteration is quite similar to that of policy evaluation. It is also an iterative algorithm. It starts with arbitrary policy values and then iteratively updates the values based on the Bellman optimality equation until they converge. So in each iteration, instead of taking the expectation (average) of values across all actions, it picks the action that achieves the maximal policy values:

Here, V*(s) denotes the optimal value, which is the value of the optimal policy; T(s, a, s') is the transition probability from state s to state s’ by taking action a; and R(s, a) is the reward received in state s by taking action a.

Once...