Reinforcement learning

Our objective is to build a neural network to play the game of catch. Each game starts with a ball being dropped from a random position from the top of the screen. The objective is to move a paddle at the bottom of the screen using the left and right arrow keys to catch the ball by the time it reaches the bottom. As games go, this is quite simple. At any point in time, the state of this game is given by the (x, y) coordinates of the ball and paddle. Most arcade games tend to have many more moving parts, so a general solution is to provide the entire current game screen image as the state. The following screenshot shows four consecutive screenshots of our catch game:

Astute readers might note that our problem could be modeled as a classification problem, where the input to the network are the game screen images and the output is one of three actions--move left, stay, or move right. However, this would require us to provide the network with training examples, possibly...