Mastering the game of Go without human knowledge

Abstract

A long-standing goal of artificial intelligence is an algorithm that learns, tabula rasa, superhuman proficiency in challenging domains. Recently, AlphaGo became the first program to defeat a world champion in the game of Go. The tree search in AlphaGo evaluated positions and selected moves using deep neural networks. These neural networks were trained by supervised learning from human expert moves, and by reinforcement learning from self-play. Here we introduce an algorithm based solely on reinforcement learning, without human data, guidance or domain knowledge beyond game rules. AlphaGo becomes its own teacher: a neural network is trained to predict AlphaGo’s own move selections and also the winner of AlphaGo’s games. This neural network improves the strength of the tree search, resulting in higher quality move selection and stronger self-play in the next iteration. Starting tabula rasa, our new program AlphaGo Zero achieved superhuman performance, winning 100–0 against the previously published, champion-defeating AlphaGo.

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Figure 1: Self-play reinforcement learning in AlphaGo Zero.
Figure 2: MCTS in AlphaGo Zero.
Figure 3: Empirical evaluation of AlphaGo Zero.
Figure 4: Comparison of neural network architectures in AlphaGo Zero and AlphaGo Lee.
Figure 5: Go knowledge learned by AlphaGo Zero.
Figure 6: Performance of AlphaGo Zero.

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Acknowledgements

We thank A. Cain for work on the visuals; A. Barreto, G. Ostrovski, T. Ewalds, T. Schaul, J. Oh and N. Heess for reviewing the paper; and the rest of the DeepMind team for their support.

Author information

D.S., J.S., K.S., I.A., A.G., L.S. and T.H. designed and implemented the reinforcement learning algorithm in AlphaGo Zero. A.H., J.S., M.L. and D.S. designed and implemented the search in AlphaGo Zero. L.B., J.S., A.H., F.H., T.H., Y.C. and D.S. designed and implemented the evaluation framework for AlphaGo Zero. D.S., A.B., F.H., A.G., T.L., T.G., L.S., G.v.d.D. and D.H. managed and advised on the project. D.S., T.G. and A.G. wrote the paper.

Correspondence to David Silver.

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Competing interests

The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks S. Singh and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Tournament games between AlphaGo Zero (20 blocks, 3 days) versus AlphaGo Lee using 2 h time controls.

One hundred moves of the first 20 games are shown; full games are provided in the Supplementary Information.

Extended Data Figure 2 Frequency of occurence over time during training, for each joseki from Fig. 5a (corner sequences common in professional play that were discovered by AlphaGo Zero).

The corresponding joseki are shown on the right.

Extended Data Figure 3 Frequency of occurence over time during training, for each joseki from Fig. 5b (corner sequences that AlphaGo Zero favoured for at least one iteration), and one additional variation.

The corresponding joseki are shown on the right.

Extended Data Figure 4 AlphaGo Zero (20 blocks) self-play games.

The 3-day training run was subdivided into 20 periods. The best player from each period (as selected by the evaluator) played a single game against itself, with 2 h time controls. One hundred moves are shown for each game; full games are provided in the Supplementary Information.

Extended Data Figure 5 AlphaGo Zero (40 blocks) self-play games.

The 40-day training run was subdivided into 20 periods. The best player from each period (as selected by the evaluator) played a single game against itself, with 2 h time controls. One hundred moves are shown for each game; full games are provided in the Supplementary Information.

Extended Data Figure 6 AlphaGo Zero (40 blocks, 40 days) versus AlphaGo Master tournament games using 2 h time controls.

One hundred moves of the first 20 games are shown; full games are provided in the Supplementary Information.

Extended Data Table 1 Move prediction accuracy
Extended Data Table 2 Game outcome prediction error
Extended Data Table 3 Learning rate schedule

Supplementary information

Reporting Summary (PDF 67 kb)

Supplementary Data

This zipped file contains the game records of self-play and tournament games played by AlphaGo Zero in .sgf format. (ZIP 82 kb)

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Silver, D., Schrittwieser, J., Simonyan, K. et al. Mastering the game of Go without human knowledge. Nature 550, 354–359 (2017). https://doi.org/10.1038/nature24270

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