In the previous chapter, we became familiar with the Bellman equation and the practical method of its application called Value iteration. This approach allowed us to significantly improve our speed and convergence in the FrozenLake environment, which is promising, but can we go further?

In this chapter, we'll try to apply the same theory to problems of much greater complexity: arcade games from the Atari 2600 platform, which are the de-facto benchmark of the RL research community. To deal with this new and more challenging goal, we'll talk about problems with the Value iteration method and introduce its variation, called Q-learning. In particular, we'll look at the application of Q-learning to so-called "grid world" environments, which is called tabular Q-learning, and then we'll discuss Q-learning in conjunction with neural networks. This combination has the name DQN. At the end of the chapter, we'll reimplement a DQN...