The theory of reinforcement learning provides a normative account1, deeply rooted in psychological2 and neuroscientific3 perspectives on animal behaviour, of how agents may optimize their control of an environment. To use reinforcement learning successfully in situations approaching real-world complexity, however, agents are confronted with a difficult task: they must derive efficient representations of the environment from high-dimensional sensory inputs, and use these to generalize past experience to new situations. Remarkably, humans and other animals seem to solve this problem through a harmonious combination of reinforcement learning and hierarchical sensory processing systems4,5, the former evidenced by a wealth of neural data revealing notable parallels between the phasic signals emitted by dopaminergic neurons and temporal difference reinforcement learning algorithms3. While reinforcement learning agents have achieved some successes in a variety of domains6,7,8, their applicability has previously been limited to domains in which useful features can be handcrafted, or to domains with fully observed, low-dimensional state spaces. Here we use recent advances in training deep neural networks9,10,11 to develop a novel artificial agent, termed a deep Q-network, that can learn successful policies directly from high-dimensional sensory inputs using end-to-end reinforcement learning. We tested this agent on the challenging domain of classic Atari 2600 games12. We demonstrate that the deep Q-network agent, receiving only the pixels and the game score as inputs, was able to surpass the performance of all previous algorithms and achieve a level comparable to that of a professional human games tester across a set of 49 games, using the same algorithm, network architecture and hyperparameters. This work bridges the divide between high-dimensional sensory inputs and actions, resulting in the first artificial agent that is capable of learning to excel at a diverse array of challenging tasks.
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We thank G. Hinton, P. Dayan and M. Bowling for discussions, A. Cain and J. Keene for work on the visuals, K. Keller and P. Rogers for help with the visuals, G. Wayne for comments on an earlier version of the manuscript, and the rest of the DeepMind team for their support, ideas and encouragement.
The authors declare no competing financial interests.
Extended data figures and tables
Extended Data Figure 1 Two-dimensional t-SNE embedding of the representations in the last hidden layer assigned by DQN to game states experienced during a combination of human and agent play in Space Invaders.
The plot was generated by running the t-SNE algorithm25 on the last hidden layer representation assigned by DQN to game states experienced during a combination of human (30 min) and agent (2 h) play. The fact that there is similar structure in the two-dimensional embeddings corresponding to the DQN representation of states experienced during human play (orange points) and DQN play (blue points) suggests that the representations learned by DQN do indeed generalize to data generated from policies other than its own. The presence in the t-SNE embedding of overlapping clusters of points corresponding to the network representation of states experienced during human and agent play shows that the DQN agent also follows sequences of states similar to those found in human play. Screenshots corresponding to selected states are shown (human: orange border; DQN: blue border).
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.
This file contains a Supplementary Discussion. (PDF 110 kb)
This video shows the performance of the DQN agent while playing the game of Space Invaders. The DQN agent successfully clears the enemy ships on the screen while the enemy ships move down and sideways with gradually increasing speed. (MOV 5106 kb)
This video shows the improvement in the performance of DQN over training (i.e. after 100, 200, 400 and 600 episodes). After 600 episodes DQN finds and exploits the optimal strategy in this game, which is to make a tunnel around the side, and then allow the ball to hit blocks by bouncing behind the wall. Note: the score is displayed at the top left of the screen (maximum for clearing one screen is 448 points), number of lives remaining is shown in the middle (starting with 5 lives), and the “1” on the top right indicates this is a 1-player game. (MOV 1500 kb)
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Mnih, V., Kavukcuoglu, K., Silver, D. et al. Human-level control through deep reinforcement learning. Nature 518, 529–533 (2015). https://doi.org/10.1038/nature14236
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