Neural networks meet tree search in Go

Policy and value networks strengthened search in a difficult board game.

David Silver and colleagues

AI topics

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The contribution

AlphaGo combined neural networks for selecting moves and evaluating positions with a tree-search procedure. The system integrated supervised learning from expert play and reinforcement learning to reach a major milestone in computer Go.

What this does not establish

This paper reports the match against Fan Hui. It does not report the later March 2016 Lee Sedol match, and it concerns a specific game.

Why this date?

The paper appeared on 27 January 2016 and reports the October 2015 Fan Hui match.

This entry follows the linked publication. Read the source and date conventions.

The original work

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

Authors: David Silver and colleagues
Publication: Nature, 529, 484–489
Source type: Journal article

Original Nature article

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Citations

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ImageNet Classification with Deep Convolutional Neural Networks (2012)
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Human-level control through deep reinforcement learning (2015)
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Reference section 1 (PDF pages 6)

1. Allis, L. V. Searching for Solutions in Games and Artificial Intelligence. PhD thesis, Univ. Limburg, Maastricht, The Netherlands (1994). 2. van den Herik, H., Uiterwijk, J. W. & van Rijswijck, J. Games solved: now and in the future. Artif. Intell. 134, 277–311 (2002). 3. Schaeffer, J. The games computers (and people) play. Advances in Computers 52, 189–266 (2000). 4. Campbell, M., Hoane, A. & Hsu, F. Deep Blue. Artif. Intell. 134, 57–83 (2002). 5. Schaeffer, J. et al. A world championship caliber checkers program. Artif. Intell. 53, 273–289 (1992). 6. Buro, M. From simple features to sophisticated evaluation functions. In 1st International Conference on Computers and Games, 126–145 (1999). 7. Müller, M. Computer Go. Artif. Intell. 134, 145–179 (2002). 8. Tesauro, G. & Galperin, G. On-line policy improvement using Monte-Carlo search. In Advances in Neural Information Processing, 1068–1074 (1996). 9. Sheppard, B. World-championship-caliber Scrabble. Artif. Intell. 134, 241–275 (2002). 10. Bouzy, B. & Helmstetter, B. Monte-Carlo Go developments. In 10th International Conference on Advances in Computer Games, 159–174 (2003). 11. Coulom, R. Efficient selectivity and backup operators in Monte-Carlo tree search. In 5th International Conference on Computers and Games, 72–83 (2006). 12. Kocsis, L. & Szepesvári, C. Bandit based Monte-Carlo planning. In 15th European Conference on Machine Learning, 282–293 (2006). 13. Coulom, R. Computing Elo ratings of move patterns in the game of Go. ICGA J. 30, 198–208 (2007). 14. Baudiš, P. & Gailly, J.-L. Pachi: State of the art open source Go program. In Advances in Computer Games, 24–38 (Springer, 2012). 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 Games 2, 259–270 (2010). 16. Gelly, S. & Silver, D. Combining online and offline learning in UCT. In 17th International Conference on Machine Learning, 273–280 (2007). 17. Krizhevsky, A., Sutskever, I. & Hinton, G. ImageNet classification with deep convolutional neural networks. In Advances in Neural Information Processing Systems, 1097–1105 (2012). 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). 19. Mnih, V. et al. Human-level control through deep reinforcement learning. Nature 518, 529–533 (2015). 20. LeCun, Y., Bengio, Y. & Hinton, G. Deep learning. Nature 521, 436–444 (2015). 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). 22. Sutskever, I. & Nair, V. Mimicking Go experts with convolutional neural networks. In International Conference on Artificial Neural Networks, 101–110 (2008). 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). 24. Clark, C. & Storkey, A. J. Training deep convolutional neural networks to play go. In 32nd International Conference on Machine Learning, 1766–1774 (2015). 25. Williams, R. J. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Mach. Learn. 8, 229–256 (1992). 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). 27. Sutton, R. & Barto, A. Reinforcement Learning: an Introduction (MIT Press, 1998). 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). 29. Enzenberger, M. Evaluation in Go by a neural network using soft segmentation. In 10th Advances in Computer Games Conference, 97–108 (2003). 267. 30. Silver, D., Sutton, R. & Müller, M. Temporal-difference search in computer Go. Mach. Learn. 87, 183–219 (2012). 31. Levinovitz, A. The mystery of Go, the ancient game that computers still can’t win. Wired Magazine (2014). 32. Mechner, D. All Systems Go. The Sciences 38, 32–37 (1998). 33. Mandziuk, J. Computational intelligence in mind games. In Challenges for Computational Intelligence, 407–442 (2007). 34. Berliner, H. A chronology of computer chess and its literature. Artif. Intell. 10, 201–214 (1978). 35. Browne, C. et al. A survey of Monte-Carlo tree search methods. IEEE Trans. Comput. Intell. AI in Games 4, 1–43 (2012). 36. Gelly, S. et al. The grand challenge of computer Go: Monte Carlo tree search and extensions. Commun. ACM 55, 106–113 (2012). 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). 38. KGS. Rating system math. http://www.gokgs.com/help/rmath.html.

Reference section 2 (PDF pages 9)

39. Littman, M. L. Markov games as a framework for multi-agent reinforcement learning. In 11th International Conference on Machine Learning, 157–163 (1994). 40. Knuth, D. E. & Moore, R. W. An analysis of alpha-beta pruning. Artif. Intell. 6, 293–326 (1975). 41. Sutton, R. Learning to predict by the method of temporal differences. Mach. Learn. 3, 9–44 (1988). 42. Baxter, J., Tridgell, A. & Weaver, L. Learning to play chess using temporal differences. Mach. Learn. 40, 243–263 (2000). 43. Veness, J., Silver, D., Blair, A. & Uther, W. Bootstrapping from game tree search. In Advances in Neural Information Processing Systems (2009). 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). 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). 46. Tesauro, G. TD-gammon, a self-teaching backgammon program, achieves master-level play. Neural Comput. 6, 215–219 (1994). 47. Dahl, F. Honte, a Go-playing program using neural nets. In Machines that learn to play games, 205–223 (Nova Science, 1999). 48. Rosin, C. D. Multi-armed bandits with episode context. Ann. Math. Artif. Intell. 61, 203–230 (2011). 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). 50. Gelly, S., Wang, Y., Munos, R. & Teytaud, O. Modification of UCT with patterns in Monte-Carlo Go. Tech. Rep. 6062, INRIA (2006). 51. Silver, D. & Tesauro, G. Monte-Carlo simulation balancing. In 26th International Conference on Machine Learning, 119 (2009). 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). 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). 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). 55. Segal, R. B. On the scalability of parallel UCT. Computers and Games 6515, 36–47 (2011). 56. Enzenberger, M. & Müller, M. A lock-free multithreaded Monte-Carlo tree search algorithm. In 12th Advances in Computer Games Conference, 14–20 (2009). 57. Huang, S.-C., Coulom, R. & Lin, S.-S. Time management for Monte-Carlo tree search applied to the game of Go. In International Conference on Technologies and Applications of Artificial Intelligence, 462–466 (2010). 58. Gelly, S. & Silver, D. Monte-Carlo tree search and rapid action value estimation in computer Go. Artif. Intell. 175, 1856–1875 (2011). 59. Baudiš, P. Balancing MCTS by dynamically adjusting the komi value. ICGA J. 34, 131 (2011).

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