Mastering the game of Go with deep neural networks and tree search

• David Silver
• , Aja Huang
• , Chris J. Maddison
• , Arthur Guez
• , Laurent Sifre
• , George van den Driessche
• ,Julian Schrittwieser
• , Ioannis Antonoglou
• , Veda Panneershelvam
• , Marc Lanctot
• , Sander Dieleman
• ,Dominik Grewe
• , John Nham
• , Nal Kalchbrenner
• , Ilya Sutskever
• , Timothy Lillicrap
• , Madeleine Leach
• ,Koray Kavukcuoglu
• , Thore Graepel
•  & Demis Hassabis

• Nature volume529, pages484–489 (28 January 2016)
• doi:10.1038/nature16961
• Download Citation
  • Computational science
  • Computer science
  • Reward

Received:

11 November 2015

Accepted:

05 January 2016

Published:

27 January 2016

Abstract

The game of Go has long been viewed as the most challenging of classic games for artificial intelligence owing to its enormous search space and the difficulty of evaluating board positions and moves. Here we introduce a new approach to computer Go that uses ‘value networks’ to evaluate board positions and ‘policy networks’ to select moves. These deep neural networks are trained by a novel combination of supervised learning from human expert games, and reinforcement learning from games of self-play. Without any lookahead search, the neural networks play Go at the level of state-of-the-art Monte Carlo tree search programs that simulate thousands of random games of self-play. We also introduce a new search algorithm that combines Monte Carlo simulation with value and policy networks. Using this search algorithm, our program AlphaGo achieved a 99.8% winning rate against other Go programs, and defeated the human European Go champion by 5 games to 0. This is the first time that a computer program has defeated a human professional player in the full-sized game of Go, a feat previously thought to be at least a decade away.

• Subscribe to Nature for full access:

  $199

  Subscribe

• READCUBE ACCESS:

  $8.99rent

  $22.00buy

  Buy/Rent now

Additional access options:

Already a subscriber?  Log in  now or  Register  for online access.

• Login via Athens | 
• Login via Shibboleth | 
• Use a document delivery service | 
• Purchase a site license

References

1. 1.

   Allis, L. V. Searching for Solutions in Games and Artificial Intelligence. PhD thesis, Univ. Limburg, Maastricht, The Netherlands (1994)

   • Show context
   • • Google Scholar
2. 2.

   van den Herik, H., Uiterwijk, J. W. & van Rijswijck, J. Games solved: now and in the future. Artif. Intell. 134, 277–311 (2002)

   • Show context
   • • Article
     • Google Scholar
3. 3.

   Schaeffer, J. The games computers (and people) play. Advances in Computers 52, 189–266 (2000)

   • Show context
   • • Google Scholar
4. 4.

   Campbell, M., Hoane, A. & Hsu, F. Deep Blue. Artif. Intell. 134, 57–83 (2002)

   • Show context
   • • Article
     • Google Scholar
5. 5.

   Schaeffer, J. et al. A world championship caliber checkers program. Artif. Intell. 53, 273–289 (1992)

   • Show context
   • • Article
     • Google Scholar
6. 6.

   Buro, M. From simple features to sophisticated evaluation functions. In 1st International Conference on Computers and Games, 126–145 (1999)

   • Show context
   • • Google Scholar
7. 7.

   Müller, M. Computer Go. Artif. Intell. 134, 145–179 (2002)

   • Show context
   • • Article
     • Google Scholar
8. 8.

   Tesauro, G. & Galperin, G. On-line policy improvement using Monte-Carlo search. In Advances in Neural Information Processing, 1068–1074 (1996)

   • Show context
   • • Google Scholar
9. 9.

   Sheppard, B. World-championship-caliber Scrabble. Artif. Intell.134, 241–275 (2002)

   • Show context
   • • Article
     • Google Scholar
10. 10.

    Bouzy, B. & Helmstetter, B. Monte-Carlo Go developments. In10th International Conference on Advances in Computer Games, 159–174 (2003)

    • Show context
    • • Google Scholar
11. 11.

    Coulom, R. Efficient selectivity and backup operators in Monte-Carlo tree search. In 5th International Conference on Computers and Games, 72–83 (2006)

    • Show context
    • • Google Scholar
12. 12.

    Kocsis, L. & Szepesvári, C. Bandit based Monte-Carlo planning. In15th European Conference on Machine Learning, 282–293 (2006)

    • Show context
    • • Google Scholar
13. 13.

    Coulom, R. Computing Elo ratings of move patterns in the game of Go. ICGA J. 30, 198–208 (2007)

    • Show context
    • • Google Scholar
14. 14.

    Baudiš, P. & Gailly, J.-L. Pachi: State of the art open source Go program. In Advances in Computer Games, 24–38 (Springer, 2012)

    • Show context
    • • Google Scholar
15. 15.

    Müller, M., Enzenberger, M., Arneson, B. & Segal, R. Fuego – an open-source framework for board games and Go engine based on Monte-Carlo tree search. IEEE Trans. Comput. Intell. AI in Games2, 259–270 (2010)

    • Show context
    • • Article
      • Google Scholar
16. 16.

    Gelly, S. & Silver, D. Combining online and offline learning in UCT. In 17th International Conference on Machine Learning, 273–280 (2007)

    • Show context
    • • Google Scholar
17. 17.

    Krizhevsky, A., Sutskever, I. & Hinton, G. ImageNet classification with deep convolutional neural networks. In Advances in Neural Information Processing Systems, 1097–1105 (2012)

    • Show context
    • • Google Scholar
18. 18.

    Lawrence, S., Giles, C. L., Tsoi, A. C. & Back, A. D. Face recognition: a convolutional neural-network approach. IEEE Trans. Neural Netw. 8, 98–113 (1997)

    • Show context
    • • PubMed
      • Article
      • Google Scholar
19. 19.

    Mnih, V. et al. Human-level control through deep reinforcement learning. Nature 518, 529–533 (2015)

    • Show context
    • • CAS
      • PubMed
      • Article
      • Google Scholar
20. 20.

    LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436–444 (2015)

    • Show context
    • • CAS
      • PubMed
      • Article
      • Google Scholar
21. 21.

    Stern, D., Herbrich, R. & Graepel, T. Bayesian pattern ranking for move prediction in the game of Go. In International Conference of Machine Learning, 873–880 (2006)

    • Show context
    • • Google Scholar
22. 22.

    Sutskever, I. & Nair, V. Mimicking Go experts with convolutional neural networks. In International Conference on Artificial Neural Networks, 101–110 (2008)

    • Show context
    • • Google Scholar
23. 23.

    Maddison, C. J., Huang, A., Sutskever, I. & Silver, D. Move evaluation in Go using deep convolutional neural networks. 3rd International Conference on Learning Representations (2015)

    • Show context
    • • Google Scholar
24. 24.

    Clark, C. & Storkey, A. J. Training deep convolutional neural networks to play go. In 32nd International Conference on Machine Learning, 1766–1774 (2015)

    • Show context
    • • Google Scholar
25. 25.

    Williams, R. J. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Mach. Learn. 8, 229–256 (1992)

    • Show context
    • • Article
      • Google Scholar
26. 26.

    Sutton, R., McAllester, D., Singh, S. & Mansour, Y. Policy gradient methods for reinforcement learning with function approximation. In Advances in Neural Information Processing Systems, 1057–1063 (2000)

    • Show context
    • • Google Scholar
27. 27.

    Sutton, R. & Barto, A. Reinforcement Learning: an Introduction(MIT Press, 1998)

    • Show context
    • • Google Scholar
28. 28.

    Schraudolph, N. N., Dayan, P. & Sejnowski, T. J. Temporal difference learning of position evaluation in the game of Go. Adv. Neural Inf. Process. Syst. 6, 817–824 (1994)

    • Show context
    • • Google Scholar
29. 29.

    Enzenberger, M. Evaluation in Go by a neural network using soft segmentation. In 10th Advances in Computer Games Conference, 97–108 (2003). 267

    • Show context
    • • Google Scholar
30. 30.

    Silver, D., Sutton, R. & Müller, M. Temporal-difference search in computer Go. Mach. Learn. 87, 183–219 (2012)

    • Show context
    • • Article
      • Google Scholar
31. 31.

    Levinovitz, A. The mystery of Go, the ancient game that computers still can’t win. Wired Magazine (2014)

    • Show context
    • • Google Scholar
32. 32.

    Mechner, D. All Systems Go. The Sciences 38, 32–37 (1998)

    • Show context
    • • Article
      • Google Scholar
33. 33.

    Mandziuk, J. Computational intelligence in mind games. InChallenges for Computational Intelligence, 407–442 (2007)

    • Show context
    • • Google Scholar
34. 34.

    Berliner, H. A chronology of computer chess and its literature.Artif. Intell. 10, 201–214 (1978)

    • Show context
    • • Article
      • Google Scholar
35. 35.

    Browne, C. et al. A survey of Monte-Carlo tree search methods.IEEE Trans. Comput. Intell. AI in Games 4, 1–43 (2012)

    • Show context
    • • Article
      • Google Scholar
36. 36.

    Gelly, S. et al. The grand challenge of computer Go: Monte Carlo tree search and extensions. Commun. ACM 55, 106–113 (2012)

    • Show context
    • • Article
      • Google Scholar
37. 37.

    Coulom, R. Whole-history rating: A Bayesian rating system for players of time-varying strength. In International Conference on Computers and Games, 113–124 (2008)

    • Show context
    • • Google Scholar
38. 38.

    KGS. Rating system math.http://www.gokgs.com/help/rmath.html

    • Show context
    • • Google Scholar
39. 39.

    Littman, M. L. Markov games as a framework for multi-agent reinforcement learning. In 11th International Conference on Machine Learning, 157–163 (1994)

    • Show context
    • • Google Scholar
40. 40.

    Knuth, D. E. & Moore, R. W. An analysis of alpha-beta pruning.Artif. Intell. 6, 293–326 (1975)

    • Show context
    • • Article
      • Google Scholar
41. 41.

    Sutton, R. Learning to predict by the method of temporal differences. Mach. Learn. 3, 9–44 (1988)

    • Show context
    • • Article
      • Google Scholar
42. 42.

    Baxter, J., Tridgell, A. & Weaver, L. Learning to play chess using temporal differences. Mach. Learn. 40, 243–263 (2000)

    • Show context
    • • Article
      • Google Scholar
43. 43.

    Veness, J., Silver, D., Blair, A. & Uther, W. Bootstrapping from game tree search. In Advances in Neural Information Processing Systems (2009)

    • Show context
    • • Google Scholar
44. 44.

    Samuel, A. L. Some studies in machine learning using the game of checkers II - recent progress. IBM J. Res. Develop. 11, 601–617 (1967)

    • Show context
    • • Article
      • Google Scholar
45. 45.

    Schaeffer, J., Hlynka, M. & Jussila, V. Temporal difference learning applied to a high-performance game-playing program. In 17th International Joint Conference on Artificial Intelligence, 529–534 (2001)

    • Show context
    • • Google Scholar
46. 46.

    Tesauro, G. TD-gammon, a self-teaching backgammon program, achieves master-level play. Neural Comput. 6, 215–219 (1994)

    • Show context
    • • Article
      • Google Scholar
47. 47.

    Dahl, F. Honte, a Go-playing program using neural nets. InMachines that learn to play games, 205–223 (Nova Science, 1999)

    • Show context
    • • Google Scholar
48. 48.

    Rosin, C. D. Multi-armed bandits with episode context. Ann. Math. Artif. Intell. 61, 203–230 (2011)

    • Show context
    • • Article
      • Google Scholar
49. 49.

    Lanctot, M., Winands, M. H. M., Pepels, T. & Sturtevant, N. R.Monte Carlo tree search with heuristic evaluations using implicit minimax backups. In IEEE Conference on Computational Intelligence and Games, 1–8 (2014)

    • Show context
    • • Google Scholar
50. 50.

    Gelly, S., Wang, Y., Munos, R. & Teytaud, O. Modification of UCT with patterns in Monte-Carlo Go. Tech. Rep. 6062, INRIA (2006)

    • Show context
    • • Google Scholar
51. 51.

    Silver, D. & Tesauro, G. Monte-Carlo simulation balancing. In 26th International Conference on Machine Learning, 119 (2009)

    • Show context
    • • Google Scholar
52. 52.

    Huang, S.-C., Coulom, R. & Lin, S.-S. Monte-Carlo simulation balancing in practice. In 7th International Conference on Computers and Games, 81–92 (Springer-Verlag, 2011)

    • Show context
    • • Google Scholar
53. 53.

    Baier, H. & Drake, P. D. The power of forgetting: improving the last-good-reply policy in Monte Carlo Go. IEEE Trans. Comput. Intell. AI in Games 2, 303–309 (2010)

    • Show context
    • • Article
      • Google Scholar
54. 54.

    Huang, S. & Müller, M. Investigating the limits of Monte-Carlo tree search methods in computer Go. In 8th International Conference on Computers and Games, 39–48 (2013)

    • Show context
    • • Google Scholar
55. 55.

    Segal, R. B. On the scalability of parallel UCT. Computers and Games 6515, 36–47 (2011)

    • Show context
    • • Google Scholar
56. 56.

    Enzenberger, M. & Müller, M. A lock-free multithreaded Monte-Carlo tree search algorithm. In 12th Advances in Computer Games Conference, 14–20 (2009)

    • Show context
    • • Google Scholar
57. 57.

    Huang, S.-C., Coulom, R. & Lin, S.-S. Time management for Monte-Carlo tree search applied to the game of Go. InInternational Conference on Technologies and Applications of Artificial Intelligence, 462–466 (2010)

    • Show context
    • • Google Scholar
58. 58.

    Gelly, S. & Silver, D. Monte-Carlo tree search and rapid action value estimation in computer Go. Artif. Intell. 175, 1856–1875 (2011)

    • Show context
    • • Article
      • Google Scholar
59. 59.

    Baudiš, P. Balancing MCTS by dynamically adjusting the komi value. ICGA J. 34, 131 (2011)

    • Show context
    • • Google Scholar
60. 60.

    Baier, H. & Winands, M. H. Active opening book application for Monte-Carlo tree search in 19×19 Go. In Benelux Conference on Artificial Intelligence, 3–10 (2011)

    • Show context
    • • Google Scholar
61. 61.

    Dean, J. et al. Large scale distributed deep networks. In Advances in Neural Information Processing Systems, 1223–1231 (2012)

    • Show context
    • • Google Scholar
62. 62.

    Go ratings. http://www.goratings.org

    • Show context
    • • Google Scholar

Download references

Acknowledgements

We thank Fan Hui for agreeing to play against AlphaGo; T. Manning for refereeing the match; R. Munos and T. Schaul for helpful discussions and advice; A. Cain and M. Cant for work on the visuals; P. Dayan, G. Wayne, D. Kumaran, D. Purves, H. van Hasselt, A. Barreto and G. Ostrovski for reviewing the paper; and the rest of the DeepMind team for their support, ideas and encouragement.

Author information

Author notes

1. • David Silver
   •  & Aja Huang

   These authors contributed equally to this work.

Affiliations

1. Google DeepMind, 5 New Street Square, London EC4A 3TW, UK

   • David Silver
   • , Aja Huang
   • , Chris J. Maddison
   • , Arthur Guez
   • , Laurent Sifre
   • ,George van den Driessche
   • , Julian Schrittwieser
   • , Ioannis Antonoglou
   • ,Veda Panneershelvam
   • , Marc Lanctot
   • , Sander Dieleman
   • , Dominik Grewe
   • ,Nal Kalchbrenner
   • , Timothy Lillicrap
   • , Madeleine Leach
   • , Koray Kavukcuoglu
   • , Thore Graepel
   •  & Demis Hassabis

2. Google, 1600 Amphitheatre Parkway, Mountain View, California 94043, USA

   • John Nham
   •  & Ilya Sutskever

Contributions

A.H., G.v.d.D., J.S., I.A., M.La., A.G., T.G. and D.S. designed and implemented the search in AlphaGo. C.J.M., A.G., L.S., A.H., I.A., V.P., S.D., D.G., N.K., I.S., K.K. and D.S. designed and trained the neural networks in AlphaGo. J.S., J.N., A.H. and D.S. designed and implemented the evaluation framework for AlphaGo. D.S., M.Le., T.L., T.G., K.K. and D.H. managed and advised on the project. D.S., T.G., A.G. and D.H. wrote the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to David Silver or Demis Hassabis.

Extended data

Extended data tables

1. 1.

   Details of match between AlphaGo and Fan Hui

2. 2.

   Input features for neural networks

3. 3.

   Supervised learning results for the policy network

4. 4.

   Input features for rollout and tree policy

5. 5.

   Parameters used by AlphaGo

6. 6.

   Results of a tournament between different Go programs

7. 7.

   Results of a tournament between different variants of AlphaGo

8. 8.

   Results of a tournament between AlphaGo and distributed AlphaGo, testing scalability with hardware

9. 9.

   Cross-table of win rates in per cent between programs

10. 10.

    Cross-table of win rates in per cent between programs in the single-machine scalability study

11. 11.

    Cross-table of win rates in per cent between programs in the distributed scalability study

Supplementary information

Zip files

1. 1.

   Supplementary Information

   This zipped file contains game records for the 5 formal match games played between AlphaGo and Fan Hui.

Rights and permissions

To obtain permission to re-use content from this article visitRightsLink.

Comments

By submitting a comment you agree to abide by our Terms andCommunity Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.