Abstract
This article shows how the performance of a Monte-Carlo Tree Search (MCTS) player for Havannah can be improved by guiding the search in the playout and selection steps of MCTS. To improve the playout step of the MCTS algorithm, we used two techniques to direct the simulations, Last-Good-Reply (LGR) and N-grams. Experiments reveal that LGR gives a significant improvement, although it depends on which LGR variant is used. Using N-grams to guide the playouts also achieves a significant increase in the winning percentage. Combining N-grams with LGR leads to a small additional improvement. To enhance the selection step of the MCTS algorithm, we initialize the visit and win counts of the new nodes based on pattern knowledge. By biasing the selection towards joint/neighbor moves, local connections, and edge/corner connections, a significant improvement in the performance is obtained. Experiments show that the best overall performance is obtained when combining the visit-and-win-count initialization with LGR and N-grams. In the best case, a winning percentage of 77.5% can be achieved against the default MCTS program.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arneson, B., Hayward, R.B., Henderson, P.: Monte Carlo Tree Search in Hex. IEEE Transactions on Computational Intelligence and AI in Games 2(4), 251–258 (2010)
Baier, H., Drake, P.D.: The Power of Forgetting: Improving the Last-Good-Reply Policy in Monte Carlo Go. IEEE Transactions on Computational Intelligence and AI in Games 2(4), 303–309 (2010)
Björnsson, Y., Finnsson, H.: CadiaPlayer: A Simulation-Based General Game Player. IEEE Transactions on Computational Intelligence and AI in Games 1(1), 4–15 (2009)
Chaslot, G.M.J.-B.: Monte-Carlo Tree Search. PhD thesis, Maastricht University, Maastricht, The Netherlands (2010)
Chaslot, G.M.J.-B., Winands, M.H.M., Uiterwijk, J.W.H.M., van den Herik, H.J., Bouzy, B.: Progressive Strategies for Monte-Carlo Tree Search. New Mathematics and Natural Computation 4(3), 343–357 (2008)
Coulom, R.: Efficient Selectivity and Backup Operators in Monte-Carlo 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)
Drake, P.D.: The Last-Good-Reply Policy for Monte-Carlo Go. ICGA Journal 32(4), 221–227 (2009)
Fossel, J.D.: Monte-Carlo Tree Search Applied to the Game of Havannah. Bachelor’s thesis, Maastricht University, Maastricht, The Netherlands (2010)
Freeling, C.: Introducing Havannah. Abstract Games 14, 14–20 (2003)
Gelly, S., Silver, D.: Combining Online and Offline Knowledge in UCT. In: Ghahramani, Z. (ed.) Proceedings of the 24th International Conference on Machine Learning, ICML 2007, pp. 273–280. ACM Press, New York (2007)
Joosten, B.: Creating a Havannah Playing Agent. Bachelor’s thesis, Maastricht University, Maastricht, The Netherlands (2009)
Knuth, D.E., Moore, R.W.: An Analysis of Alpha-Beta Pruning. Artificial Intelligence 6(4), 293–326 (1975)
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)
Laramée, F.D.: Using N-Gram Statistical Models to Predict Player Behavior. In: Rabin, S. (ed.) AI Game Programming Wisdom, pp. 596–601. Charles River Media, Hingham (2002)
Lee, C.-S., Wang, M.-H., Chaslot, G.M.J.-B., Hoock, J.-B., Rimmel, A., Teytaud, O., Tsai, S.-R., Hsu, S.-C., Hong, T.-P.: The Computational Intelligence of MoGo Revealed in Taiwan’s Computer Go Tournaments. IEEE Transactions on Computational Intelligence and AI in Games 1(1), 73–89 (2009)
Lorentz, R.J.: Improving Monte–Carlo Tree Search in Havannah. In: van den Herik, H.J., Iida, H., Plaat, A. (eds.) CG 2010. LNCS, vol. 6515, pp. 105–115. Springer, Heidelberg (2011)
Nijssen, J(P.) A.M., Winands, M.H.M.: Enhancements for Multi-Player Monte-Carlo Tree Search. In: van den Herik, H.J., Iida, H., Plaat, A. (eds.) CG 2010. LNCS, vol. 6515, pp. 238–249. Springer, Heidelberg (2011)
Rimmel, A., Teytaud, F.: Multiple Overlapping Tiles for Contextual Monte Carlo Tree Search. In: Di Chio, C., Cagnoni, S., Cotta, C., Ebner, M., Ekárt, A., Esparcia-Alcazar, A.I., Goh, C.-K., Merelo, J.J., Neri, F., Preuß, M., Togelius, J., Yannakakis, G.N. (eds.) EvoApplicatons 2010. LNCS, vol. 6024, pp. 201–210. Springer, Heidelberg (2010)
Rimmel, A., Teytaud, F., Teytaud, O.: Biasing Monte-Carlo Simulations through RAVE Values. In: van den Herik, H.J., Iida, H., Plaat, A. (eds.) CG 2010. LNCS, vol. 6515, pp. 59–68. Springer, Heidelberg (2011)
Shannon, C.E.: Predication and Entropy of Printed English. The Bell System Technical Journal 30(1), 50–64 (1951)
Stankiewicz, J.A.: Knowledge-based Monte-Carlo Tree Search in Havannah. Master’s thesis, Maastricht University, Maastricht, The Netherlands (2011)
Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press, Cambridge (1998)
Teytaud, F., Teytaud, O.: Creating an Upper-Confidence-Tree Program for Havannah. In: van den Herik, H.J., Spronck, P. (eds.) ACG 2009. LNCS, vol. 6048, pp. 65–74. Springer, Heidelberg (2010)
Teytaud, F., Teytaud, O.: On the Huge Benefit of Decisive Moves in Monte-Carlo Tree Search Algorithms. In: Yannakakis, G.N., Togelius, J. (eds.) Proceedings of the 2010 IEEE Conference on Computational Intelligence and Games (CIG 2010), pp. 359–364. IEEE Press (2010)
Winands, M.H.M., Björnsson, Y.: αβ-based Play-outs in Monte-Carlo Tree Search. In: 2011 IEEE Conference on Computational Intelligence and Games (CIG 2011), pp. 110–117. IEEE Press (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Stankiewicz, J.A., Winands, M.H.M., Uiterwijk, J.W.H.M. (2012). Monte-Carlo Tree Search Enhancements for Havannah. In: van den Herik, H.J., Plaat, A. (eds) Advances in Computer Games. ACG 2011. Lecture Notes in Computer Science, vol 7168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31866-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-31866-5_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31865-8
Online ISBN: 978-3-642-31866-5
eBook Packages: Computer ScienceComputer Science (R0)