Categorical DQN

The last, and the most complicated, method in our DQN improvements toolbox is from a very recent paper, published by DeepMind in June 2017, called A Distributional Perspective on Reinforcement Learning ([9] Bellemare, Dabney, and Munos, 2017).

In the paper, the authors questioned the fundamental piece of Q-learning—Q-values—and tried to replace them with a more generic Q-value probability distribution. Let's try to understand the idea. Both the Q-learning and value iteration methods work with the values of the actions or states represented as simple numbers and showing how much total reward we can achieve from a state, or an action and a state. However, is it practical to squeeze all future possible rewards into one number? In complicated environments, the future could be stochastic, giving us different values with different probabilities.

For example, imagine the commuter scenario when you regularly drive from home to work. Most of the time...