Abstract
Risk is a complex strategy game that may be easier to understand for humans than chess but harder to deal with for computers. The main reasons are the stochastic nature of battles and the different decisions that must be coordinated within turns. Our goal is to create an artificial intelligence able to play the game without human knowledge using the Expert Iteration [1] framework. We use graph neural networks [13, 15, 22, 30] to learn the policies for the different decisions and the value estimation. Experiments on a synthetic board show that with this framework the model can rapidly learn a good country drafting policy, while the main game phases remain a challenge.
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References
Anthony, T., Tian, Z., Barber, D.: Thinking fast and slow with deep learning and tree search. arXiv preprint arXiv:1705.08439 (2017)
Anthony, T.W.: Expert iteration. Ph.D. thesis, UCL (University College London) (2021)
Auer, P., Cesa-Bianchi, N., Fischer, P.: Finite-time analysis of the multiarmed bandit problem. Mach. Learn. 47(2), 235–256 (2002)
Blomqvist, E.: Playing the game of risk with an alphazero agent (2020)
Browne, C.B., et al.: A survey of monte carlo tree search methods. IEEE Trans. Comput. Intell. AI Games 4(1), 1–43 (2012)
Carr, J.: Using graph convolutional networks and td (\(\lambda \)) to play the game of risk. arXiv preprint arXiv:2009.06355 (2020)
Cazenave, T.: Residual networks for computer go. IEEE Trans. Games 10(1), 107–110 (2018)
Cazenave, T., et al.: Polygames: Improved zero learning. ICGA J. 42(4), 244–256 (2020)
Coulom, R.: Efficient selectivity and backup operators Monte Carlo in tree search. In: van den Herik, H.J., Ciancarini, P., Donkers, H.H.L.M.J. (eds.) CG 2006. LNCS, vol. 4630, pp. 72–83. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75538-8_7
Gibson, R., Desai, N., Zhao, R.: An automated technique for drafting territories in the board game risk. In: Proceedings of the AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment. vol. 5 (2010)
Johansson, S.J., Olsson, F.: Using multi-agent system technologies in risk bots. In: Proceedings of the Second Artificial Intelligence and Interactive Digital Entertainment Conference (AIIDE), Marina del Rey (2006)
Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)
Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016)
Kocsis, L., Szepesvári, C.: Bandit based Monte-Carlo planning. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) ECML 2006. LNCS (LNAI), vol. 4212, pp. 282–293. Springer, Heidelberg (2006). https://doi.org/10.1007/11871842_29
Li, G., Muller, M., Thabet, A., Ghanem, B.: Deepgcns: Can GCNS GO as deep as CNNS? In: Proceedings of the IEEE/CVF International Conference on Computer Vision, pp. 9267–9276 (2019)
Li, G., Xiong, C., Thabet, A., Ghanem, B.: DeeperGCN: all you need to train deeper GCNs. arXiv preprint arXiv:2006.07739 (2020)
Lütolf, M.: A Learning AI for the game Risk using the TD (\(\lambda \))-Algorithm. Ph.D. thesis, BS Thesis, University of Basel (2013)
Melkó, E., Nagy, B.: Optimal strategy in games with chance nodes. Acta Cybernet. 18(2), 171–192 (2007)
Nijssen, J., Winands, M.H.: Search policies in multi-player games1. J. Int. Comput. Games Assoc. 36(1), 3–21 (2013)
Olsson, F.: A multi-agent system for playing the board game risk (2005)
Rosin, C.D.: Multi-armed bandits with episode context. Ann. Math. Artif. Intell. 61(3), 203–230 (2011)
Scarselli, F., Gori, M., Tsoi, A.C., Hagenbuchner, M., Monfardini, G.: The graph neural network model. IEEE Trans. Neural Netw. 20(1), 61–80 (2008)
Silver, D., et al.: Mastering the game of go with deep neural networks and tree search. Nature 529(7587), 484–489 (2016)
Silver, D., et al.: A general reinforcement learning algorithm that masters chess, shogi, and go through self-play. Science 362(6419), 1140–1144 (2018)
Silver, D., et al.: Mastering the game of go without human knowledge. Nature 550(7676), 354–359 (2017)
Soemers, D.J., Piette, E., Stephenson, M., Browne, C.: Manipulating the distributions of experience used for self-play learning in expert iteration. In: 2020 IEEE Conference on Games (CoG), pp. 245–252. IEEE (2020)
Sturtevant, N.: A comparison of algorithms for multi-player games. In: Schaeffer, J., Müller, M., Björnsson, Y. (eds.) CG 2002. LNCS, vol. 2883, pp. 108–122. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-40031-8_8
Wolf, M.: An intelligent artificial player for the game of risk. Unpublished doctoral dissertation). TU Darmstadt, Knowledge Engineering Group, Darmstadt Germany (2005). http://www.ke.tu-darmstadt.de/bibtex/topics/single/32/type
Wu, D.J.: Accelerating self-play learning in go. arXiv preprint arXiv:1902.10565 (2019)
Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C., Philip, S.Y.: A comprehensive survey on graph neural networks. IEEE Trans. Neural Netw. Learn. Syst. 32(1), 4–24 (2020)
Zhang, S., Tong, H., Xu, J., Maciejewski, R.: Graph convolutional networks: a comprehensive review. Comput. Soc. Netw. 6(1), 1–23 (2019). https://doi.org/10.1186/s40649-019-0069-y
Acknowledgment
This work was supported in part by the French government under management of Agence Nationale de la Recherche as part of the “Investissements d’avenir" program, reference ANR19-P3IA-0001 (PRAIRIE 3IA Institute).
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Heredia, L.G., Cazenave, T. (2022). Expert Iteration for Risk. In: Browne, C., Kishimoto, A., Schaeffer, J. (eds) Advances in Computer Games. ACG 2021. Lecture Notes in Computer Science, vol 13262. Springer, Cham. https://doi.org/10.1007/978-3-031-11488-5_3
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