a, A visualization of the learned value function on the game Breakout. At time points 1 and 2, the state value is predicted to be ∼17 and the agent is clearing the bricks at the lowest level. Each of the peaks in the value function curve corresponds to a reward obtained by clearing a brick. At time point 3, the agent is about to break through to the top level of bricks and the value increases to ∼21 in anticipation of breaking out and clearing a large set of bricks. At point 4, the value is above 23 and the agent has broken through. After this point, the ball will bounce at the upper part of the bricks clearing many of them by itself. b, A visualization of the learned action-value function on the game Pong. At time point 1, the ball is moving towards the paddle controlled by the agent on the right side of the screen and the values of all actions are around 0.7, reflecting the expected value of this state based on previous experience. At time point 2, the agent starts moving the paddle towards the ball and the value of the ‘up’ action stays high while the value of the ‘down’ action falls to −0.9. This reflects the fact that pressing ‘down’ would lead to the agent losing the ball and incurring a reward of −1. At time point 3, the agent hits the ball by pressing ‘up’ and the expected reward keeps increasing until time point 4, when the ball reaches the left edge of the screen and the value of all actions reflects that the agent is about to receive a reward of 1. Note, the dashed line shows the past trajectory of the ball purely for illustrative purposes (that is, not shown during the game). With permission from Atari Interactive, Inc.