iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://unpaywall.org/10.1038/NATURE24270
Mastering the game of Go without human knowledge | Nature
Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Mastering the game of Go without human knowledge

Nature volume 550, pages 354–359 (2017)Cite this article

Subjects

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

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.

Similar content being viewed by others

References

  1. Friedman, J., Hastie, T. & Tibshirani, R. The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Springer, 2009)

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

    Article  CAS  ADS  Google Scholar 

  3. Krizhevsky, A., Sutskever, I. & Hinton, G. ImageNet classification with deep convolutional neural networks. In Adv. Neural Inf. Process. Syst. Vol. 25 (eds Pereira, F., Burges, C. J. C., Bottou, L. & Weinberger, K. Q. ) 1097–1105 (2012)

  4. He, K., Zhang, X., Ren, S . & Sun, J. Deep residual learning for image recognition. In Proc. 29th IEEE Conf. Comput. Vis. Pattern Recognit. 770–778 (2016)

  5. Hayes-Roth, F., Waterman, D. & Lenat, D. Building Expert Systems (Addison-Wesley, 1984)

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

    Article  CAS  ADS  Google Scholar 

  7. Guo, X., Singh, S. P., Lee, H., Lewis, R. L. & Wang, X. Deep learning for real-time Atari game play using offline Monte-Carlo tree search planning. In Adv. Neural Inf. Process. Syst. Vol. 27 (eds Ghahramani, Z., Welling, M., Cortes, C., Lawrence, N. D. & Weinberger, K. Q. ) 3338–3346 (2014)

  8. Mnih, V . et al. Asynchronous methods for deep reinforcement learning. In Proc. 33rd Int. Conf. Mach. Learn. Vol. 48 (eds Balcan, M. F. & Weinberger, K. Q. ) 1928–1937 (2016)

  9. Jaderberg, M . et al. Reinforcement learning with unsupervised auxiliary tasks. In 5th Int. Conf. Learn. Representations (2017)

  10. Dosovitskiy, A. & Koltun, V. Learning to act by predicting the future. In 5th Int. Conf. Learn. Representations (2017)

  11. Man´dziuk, J. in Challenges for Computational Intelligence ( Duch, W. & Man´dziuk, J. ) 407–442 (Springer, 2007)

  12. Silver, D. et al. Mastering the game of Go with deep neural networks and tree search. Nature 529, 484–489 (2016)

    Article  CAS  ADS  Google Scholar 

  13. Coulom, R. Efficient selectivity and backup operators in Monte-Carlo tree search. In 5th Int. Conf. Computers and Games (eds Ciancarini, P. & van den Herik, H. J. ) 72–83 (2006)

  14. Kocsis, L. & Szepesvári, C. Bandit based Monte-Carlo planning. In 15th Eu. Conf. Mach. Learn. 282–293 (2006)

  15. Browne, C. et al. A survey of Monte Carlo tree search methods. IEEE Trans. Comput. Intell. AI Games 4, 1–49 (2012)

    Article  Google Scholar 

  16. Fukushima, K. Neocognitron: a self organizing neural network model for a mechanism of pattern recognition unaffected by shift in position. Biol. Cybern. 36, 193–202 (1980)

    Article  CAS  Google Scholar 

  17. LeCun, Y. & Bengio, Y. in The Handbook of Brain Theory and Neural Networks Ch. 3 (ed. Arbib, M. ) 276–278 (MIT Press, 1995)

  18. Ioffe, S. & Szegedy, C. Batch normalization: accelerating deep network training by reducing internal covariate shift. In Proc. 32nd Int. Conf. Mach. Learn. Vol. 37 448–456 (2015)

  19. Hahnloser, R. H. R., Sarpeshkar, R., Mahowald, M. A., Douglas, R. J. & Seung, H. S. Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit. Nature 405, 947–951 (2000)

    Article  CAS  ADS  Google Scholar 

  20. Howard, R. Dynamic Programming and Markov Processes (MIT Press, 1960)

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

  22. Bertsekas, D. P. Approximate policy iteration: a survey and some new methods. J. Control Theory Appl. 9, 310–335 (2011)

    Article  MathSciNet  Google Scholar 

  23. Scherrer, B. Approximate policy iteration schemes: a comparison. In Proc. 31st Int. Conf. Mach. Learn. Vol. 32 1314–1322 (2014)

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

    Article  MathSciNet  Google Scholar 

  25. Coulom, R. Whole-history rating: a Bayesian rating system for players of time-varying strength. In Int. Conf. Comput. Games (eds van den Herik, H. J., Xu, X . Ma, Z . & Winands, M. H. M. ) Vol. 5131 113–124 (Springer, 2008)

  26. Laurent, G. J., Matignon, L. & Le Fort-Piat, N. The world of independent learners is not Markovian. Int. J. Knowledge-Based Intelligent Engineering Systems 15, 55–64 (2011)

    Article  Google Scholar 

  27. Foerster, J. N . et al. Stabilising experience replay for deep multi-agent reinforcement learning. In Proc. 34th Int. Conf. Mach. Learn. Vol. 70 1146–1155 (2017)

  28. Heinrich, J . & Silver, D. Deep reinforcement learning from self-play in imperfect-information games. In NIPS Deep Reinforcement Learning Workshop (2016)

  29. Jouppi, N. P . et al. In-datacenter performance analysis of a Tensor Processing Unit. Proc. 44th Annu. Int. Symp. Comp. Architecture Vol. 17 1–12 (2017)

  30. Maddison, C. J., Huang, A., Sutskever, I . & Silver, D. Move evaluation in Go using deep convolutional neural networks. In 3rd Int. Conf. Learn. Representations. (2015)

  31. Clark, C . & Storkey, A. J. Training deep convolutional neural networks to play Go. In Proc. 32nd Int. Conf. Mach. Learn. Vol. 37 1766–1774 (2015)

  32. Tian, Y. & Zhu, Y. Better computer Go player with neural network and long-term prediction. In 4th Int. Conf. Learn. Representations (2016)

  33. Cazenave, T. Residual networks for computer Go. IEEE Trans. Comput. Intell. AI Games https://doi.org/10.1109/TCIAIG.2017.2681042 (2017)

  34. Huang, A. AlphaGo master online series of games. https://deepmind.com/research/AlphaGo/match-archive/master (2017)

  35. Barto, A. G. & Duff, M. Monte Carlo matrix inversion and reinforcement learning. Adv. Neural Inf. Process. Syst. 6, 687–694 (1994)

    Google Scholar 

  36. Singh, S. P. & Sutton, R. S. Reinforcement learning with replacing eligibility traces. Mach. Learn. 22, 123–158 (1996)

    MATH  Google Scholar 

  37. Lagoudakis, M. G. & Parr, R. Reinforcement learning as classification: leveraging modern classifiers. In Proc. 20th Int. Conf. Mach. Learn. 424–431 (2003)

  38. Scherrer, B., Ghavamzadeh, M., Gabillon, V., Lesner, B. & Geist, M. Approximate modified policy iteration and its application to the game of Tetris. J. Mach. Learn. Res. 16, 1629–1676 (2015)

    MathSciNet  MATH  Google Scholar 

  39. Littman, M. L. Markov games as a framework for multi-agent reinforcement learning. In Proc. 11th Int. Conf. Mach. Learn. 157–163 (1994)

  40. Enzenberger, M. The integration of a priori knowledge into a Go playing neural network. http://www.cgl.ucsf.edu/go/Programs/neurogo-html/neurogo.html (1996)

  41. Enzenberger, M. in Advances in Computer Games (eds Van Den Herik, H. J., Iida, H. & Heinz, E. A. ) 97–108 (2003)

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

    Google Scholar 

  43. 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)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  45. Silver, D. Reinforcement Learning and Simulation-Based Search in Computer Go. PhD thesis, Univ. Alberta, Edmonton, Canada (2009)

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

    Article  MathSciNet  Google Scholar 

  47. Coulom, R. Computing Elo ratings of move patterns in the game of Go. Int. Comput. Games Assoc. J. 30, 198–208 (2007)

    Google Scholar 

  48. Gelly, S., Wang, Y., Munos, R. & Teytaud, O. Modification of UCT with patterns in Monte-Carlo Go. Report No. 6062 (INRIA, 2006)

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

    Article  Google Scholar 

  50. Veness, J., Silver, D., Blair, A. & Uther, W. Bootstrapping from game tree search. In Adv. Neural Inf. Process. Syst. 1937–1945 (2009)

  51. Lai, M. Giraffe: Using Deep Reinforcement Learning to Play Chess. MSc thesis, Imperial College London (2015)

  52. Schaeffer, J., Hlynka, M . & Jussila, V. Temporal difference learning applied to a high-performance game-playing program. In Proc. 17th Int. Jt Conf. Artif. Intell. Vol. 1 529–534 (2001)

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

    Article  Google Scholar 

  54. Buro, M. From simple features to sophisticated evaluation functions. In Proc. 1st Int. Conf. Comput. Games 126–145 (1999)

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

    Article  Google Scholar 

  56. Moravcˇík, M. et al. DeepStack: expert-level artificial intelligence in heads-up no-limit poker. Science 356, 508–513 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  57. Tesauro, G & Galperin, G. On-line policy improvement using Monte-Carlo search. In Adv. Neural Inf. Process. Syst. 1068–1074 (1996)

  58. Tesauro, G. Neurogammon: a neural-network backgammon program. In Proc. Int. Jt Conf. Neural Netw. Vol. 3, 33–39 (1990)

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

    Article  Google Scholar 

  60. Kober, J., Bagnell, J. A. & Peters, J. Reinforcement learning in robotics: a survey. Int. J. Robot. Res. 32, 1238–1274 (2013)

    Article  Google Scholar 

  61. Zhang, W. & Dietterich, T. G. A reinforcement learning approach to job-shop scheduling. In Proc. 14th Int. Jt Conf. Artif. Intell. 1114–1120 (1995)

  62. Cazenave, T., Balbo, F. & Pinson, S. Using a Monte-Carlo approach for bus regulation. In Int. IEEE Conf. Intell. Transport. Syst. 1–6 (2009)

  63. Evans, R. & Gao, J. Deepmind AI reduces Google data centre cooling bill by 40%. https://deepmind.com/blog/deepmind-ai-reduces-google-data-centre-cooling-bill-40/ (2016)

  64. Abe, N . et al. Empirical comparison of various reinforcement learning strategies for sequential targeted marketing. In IEEE Int. Conf. Data Mining 3–10 (2002)

  65. Silver, D., Newnham, L., Barker, D., Weller, S. & McFall, J. Concurrent reinforcement learning from customer interactions. In Proc. 30th Int. Conf. Mach. Learn. Vol. 28 924–932 (2013)

  66. Tromp, J. Tromp–Taylor rules. http://tromp.github.io/go.html (1995)

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

    Article  Google Scholar 

  68. Shahriari, B., Swersky, K., Wang, Z., Adams, R. P. & de Freitas, N. Taking the human out of the loop: a review of Bayesian optimization. Proc. IEEE 104, 148–175 (2016)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

Download references

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

Author notes

  1. David Silver, Julian Schrittwieser and Karen Simonyan: These authors contributed equally to this work.

Authors and Affiliations

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

    David Silver, Julian Schrittwieser, Karen Simonyan, Ioannis Antonoglou, Aja Huang, Arthur Guez, Thomas Hubert, Lucas Baker, Matthew Lai, Adrian Bolton, Yutian Chen, Timothy Lillicrap, Fan Hui, Laurent Sifre, George van den Driessche, Thore Graepel & Demis Hassabis

Authors
  1. David Silver
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Julian Schrittwieser
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Karen Simonyan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ioannis Antonoglou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Aja Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Arthur Guez
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Thomas Hubert
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Lucas Baker
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Matthew Lai
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Adrian Bolton
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Yutian Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Timothy Lillicrap
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Fan Hui
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. Laurent Sifre
    View author publications

    You can also search for this author in PubMed Google Scholar

  15. George van den Driessche
    View author publications

    You can also search for this author in PubMed Google Scholar

  16. Thore Graepel
    View author publications

    You can also search for this author in PubMed Google Scholar

  17. Demis Hassabis
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

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.

Corresponding author

Correspondence to David Silver.

Ethics declarations

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.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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
Full size table
Extended Data Table 2 Game outcome prediction error
Full size table
Extended Data Table 3 Learning rate schedule
Full size table

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)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature24270

Search

Advanced search

Quick links

Nature Briefing AI and Robotics

Sign up for the Nature Briefing: AI and Robotics newsletter — what matters in AI and robotics research, free to your inbox weekly.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing: AI and Robotics