MCTS Experiments on the Voronoi Game
Conference paper
Abstract
Monte-Carlo Tree Search (MCTS) is a powerful tool in games with a finite branching factor. The paper describes an artificial player playing the Voronoi game, a game with an infinite branching factor. First, it shows how to use MCTS on a discretization of the Voronoi game, and the effects of enhancements such as RAVE and Gaussian processes (GP). Then a set of experimental results shows that MCTS with UCB+RAVE or with UCB+GP are good first solutions for playing the Voronoi game without domain-dependent knowledge. Moreover, the paper shows how the playing level can be greatly improved by using geometrical knowledge about Voronoi diagrams. The balance of diagrams is the key concept. A new set of experimental results shows that a player using MCTS and geometrical knowledge outperforms a player without knowledge.
Keywords
Gaussian Process Voronoi Diagram Gravity Center Balance Cell Bandit Problem
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References
- 1.Ahn, H.-K., Cheng, S.-W., Cheong, O., Golin, M., van Oostrum, R.: Competitive facility location: the Voronoi game. Theoretical Computer Science 310(1-3), 457–467 (2004)MathSciNetMATHCrossRefGoogle Scholar
- 2.Anuth, J.: Strategien fur das Voronoi-spiel. Master’s thesis, FernUniveristät in Hagen (July 2007)Google Scholar
- 3.Auer, P., Ortner, R., Szepesvári, C.: Improved Rates for the Stochastic Continuum-Armed Bandit Problem. In: Bshouty, N., Gentile, C. (eds.) COLT 2007. LNCS (LNAI), vol. 4539, pp. 454–468. Springer, Heidelberg (2007)CrossRefGoogle Scholar
- 4.Aurenhammer, F.: Voronoi diagrams: a survey of a fundamental geometric data structure. ACM Computing Surveys 23(3), 345–405 (1991)CrossRefGoogle Scholar
- 5.Bouzy, B.: Associating domain-dependent knowledge and Monte-Carlo approaches within a go playing program. Information Sciences 175(4), 247–257 (2005)CrossRefGoogle Scholar
- 6.Brochu, E., Cora, V., de Freitas, N.: A tutorial on bayesian optimization of expensive cost functions, with application to active user modeling and hierarchical reinforcement learning. Technical Report 23, Univ. of Brit. Col. (2009)Google Scholar
- 7.Bubeck, S., Munos, R., Stoltz, G., Szepesvári, C.: X-armed bandits. Journal of Machine Learning Research 12, 1655–1695 (2011)Google Scholar
- 8.Chaslot, G.: Monte-Carlo Tree Search. PhD thesis, Maastricht Univ (2010)Google Scholar
- 9.Chaslot, G., Winands, M., van den Herik, J., Uiterwijk, J., Bouzy, B.: Progressive strategies for Monte-Carlo tree search. New Mathematics and Natural Computation 4(3), 343–357 (2008)MathSciNetMATHCrossRefGoogle Scholar
- 10.Cheong, O., Har-Peled, S., Linial, N., Matoušek, J.: The one-round Voronoi game. In: 18th Symposium on Computational Geometry, pp. 97–101. ACM (2002)Google Scholar
- 11.Couëtoux, A., Hoock, J.-B., Sokolovska, N., Teytaud, O., Bonnard, N.: Continuous Upper Confidence Trees. In: Coello, C.A.C. (ed.) LION 2011. LNCS, vol. 6683, pp. 433–445. Springer, Heidelberg (2011)CrossRefGoogle Scholar
- 12.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)CrossRefGoogle Scholar
- 13.Dehne, F., Klein, R., Seidel, R.: Maximizing a Voronoi Region: The Convex Case. In: Bose, P., Morin, P. (eds.) ISAAC 2002. LNCS, vol. 2518, pp. 624–634. Springer, Heidelberg (2002)CrossRefGoogle Scholar
- 14.Faidley, M., Poultney, C., Shasha, D.: The Voronoi game, http://home.dti.net/crispy/Voronoi.html
- 15.Fekete, S.P., Meijer, H.: The one-round Voronoi game replayed. Computational Geometry Theory Appl. 30, 81–94 (2005)MathSciNetMATHCrossRefGoogle Scholar
- 16.Fortune, S.: A sweepline algorithm for Voronoi diagrams. Algorithmica 2(2), 153–174 (1987)MathSciNetMATHCrossRefGoogle Scholar
- 17.Gelly, S., Silver, D.: Achieving master level play in 9x9 computer go. In: AAAI, pp. 1537–1540 (2008)Google Scholar
- 18.Guibas, L.J., Stolfi, J.: Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams. In: 15th ACM Symposium on Theory Of Computing, pp. 221–234. ACM (1983)Google Scholar
- 19.Kleinberg, R.: Nearly tight bounds for the continuum-armed bandit problem. In: NIPS 17, pp. 697–704. MIT Press (2005)Google Scholar
- 20.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)CrossRefGoogle Scholar
- 21.Lloyd, S.P.: Least squares quantization in PCM. IEEE Transactions on Information Theory 28, 129–137 (1982)MathSciNetMATHCrossRefGoogle Scholar
- 22.Mostafavi, M.A., Gold, C., Dakowicz, M.: Delete and insert operations in Voronoi/Delaunay methods and applications. Computers and Geosciences 29(4), 523–530 (2003)CrossRefGoogle Scholar
- 23.Edward Rasmussen, C., Williams, C.K.I.: GaussianProcesses for Machine Learning. MIT Press (2006)Google Scholar
- 24.Selimi, I.: The Voronoi game (2008), http://www.voronoigame.com/
- 25.Shewchuk, J.: Triangle: Engineering a 2d Quality Mesh Generator and Delaunay Triangulator. In: Lin, M.C., Manocha, D. (eds.) FCRC-WS 1996 and WACG 1996. LNCS, vol. 1148, pp. 203–222. Springer, Heidelberg (1996)CrossRefGoogle Scholar
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