Skip to main content

Expert Iteration for Risk

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13262))

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.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    https://github.com/lucasgneccoh/pyLux.

  2. 2.

    https://sillysoft.net/lux/.

References

  1. Anthony, T., Tian, Z., Barber, D.: Thinking fast and slow with deep learning and tree search. arXiv preprint arXiv:1705.08439 (2017)

  2. Anthony, T.W.: Expert iteration. Ph.D. thesis, UCL (University College London) (2021)

    Google Scholar 

  3. Auer, P., Cesa-Bianchi, N., Fischer, P.: Finite-time analysis of the multiarmed bandit problem. Mach. Learn. 47(2), 235–256 (2002)

    Article  Google Scholar 

  4. Blomqvist, E.: Playing the game of risk with an alphazero agent (2020)

    Google Scholar 

  5. Browne, C.B., et al.: A survey of monte carlo tree search methods. IEEE Trans. Comput. Intell. AI Games 4(1), 1–43 (2012)

    Google Scholar 

  6. Carr, J.: Using graph convolutional networks and td (\(\lambda \)) to play the game of risk. arXiv preprint arXiv:2009.06355 (2020)

  7. Cazenave, T.: Residual networks for computer go. IEEE Trans. Games 10(1), 107–110 (2018)

    Article  Google Scholar 

  8. Cazenave, T., et al.: Polygames: Improved zero learning. ICGA J. 42(4), 244–256 (2020)

    Article  Google Scholar 

  9. 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

    Chapter  Google Scholar 

  10. 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)

    Google Scholar 

  11. 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)

    Google Scholar 

  12. Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)

  13. Kipf, T.N., Welling, M.: Semi-supervised classification with graph convolutional networks. arXiv preprint arXiv:1609.02907 (2016)

  14. 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

    Chapter  Google Scholar 

  15. 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)

    Google Scholar 

  16. Li, G., Xiong, C., Thabet, A., Ghanem, B.: DeeperGCN: all you need to train deeper GCNs. arXiv preprint arXiv:2006.07739 (2020)

  17. Lütolf, M.: A Learning AI for the game Risk using the TD (\(\lambda \))-Algorithm. Ph.D. thesis, BS Thesis, University of Basel (2013)

    Google Scholar 

  18. Melkó, E., Nagy, B.: Optimal strategy in games with chance nodes. Acta Cybernet. 18(2), 171–192 (2007)

    MathSciNet  MATH  Google Scholar 

  19. Nijssen, J., Winands, M.H.: Search policies in multi-player games1. J. Int. Comput. Games Assoc. 36(1), 3–21 (2013)

    Google Scholar 

  20. Olsson, F.: A multi-agent system for playing the board game risk (2005)

    Google Scholar 

  21. Rosin, C.D.: Multi-armed bandits with episode context. Ann. Math. Artif. Intell. 61(3), 203–230 (2011)

    Article  MathSciNet  Google Scholar 

  22. 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)

    Article  Google Scholar 

  23. Silver, D., et al.: Mastering the game of go with deep neural networks and tree search. Nature 529(7587), 484–489 (2016)

    Google Scholar 

  24. Silver, D., et al.: A general reinforcement learning algorithm that masters chess, shogi, and go through self-play. Science 362(6419), 1140–1144 (2018)

    Article  MathSciNet  Google Scholar 

  25. Silver, D., et al.: Mastering the game of go without human knowledge. Nature 550(7676), 354–359 (2017)

    Google Scholar 

  26. 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)

    Google Scholar 

  27. 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

    Chapter  Google Scholar 

  28. 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

  29. Wu, D.J.: Accelerating self-play learning in go. arXiv preprint arXiv:1902.10565 (2019)

  30. 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)

    Article  MathSciNet  Google Scholar 

  31. 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

    Article  Google Scholar 

Download references

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).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tristan Cazenave .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

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

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-11488-5_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-11487-8

  • Online ISBN: 978-3-031-11488-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics