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

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

由 烂漫一生 提交于 2020-04-25 17:00:46

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

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.

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    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

      • 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.

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