Synonyms
Definition
Monte-Carlo Tree Search (MCTS) (Coulom 2007; Kocsis et al. 2006) is a best-first search method that does not require a positional evaluation function. It is based on a randomized exploration of the search space. Using the results of previous explorations, the algorithm gradually builds up a game tree in memory and successively becomes better at accurately estimating the values of the most promising moves. MCTS consists of four strategic steps, repeated as long as there is time left (Chaslot et al. 2008b). The steps, outlined in Fig. 1, are as follows:
References and Further Reading
Abramson, B.: Expected-outcome: A general model of static evaluation. IEEE Trans. Pattern Anal. Mach. Intell. 12(2), 182–193 (1990)
Arneson, B., Hayward, R.B., Henderson, P.: Monte Carlo Tree Search in Hex. IEEE Trans. Comput. Intell. AI Games 2(4), 251–258 (2010)
Auer, P., Cesa-Bianchi, N., Fischer, P.: Finite-time analysis of the multiarmed bandit problem. Mach. Learn. 47(2–3), 235–256 (2002)
Balla, R.K., Fern A.: UCT for tactical assault planning in real-time strategy games. In: Boutilier, C. (ed.) Proceedings of the Twenty-First International Joint Conference on Artificial Intelligence (IJCAI-09), pp. 40–45. AAAI Press, Menlo Park, CA, USA (2009)
Billings, D., Peña, L., Schaeffer, J., Szafron, D.: Using probabilistic knowledge and simulation to play poker. In: Hendler, J., Subramanian, D. (eds) Proceedings of the Sixteenth National Conference on Artificial Intelligence and Eleventh Conference on Innovative Applications of Artificial Intelligence, pp. 697–703. AAAI Press/The MIT Press, Menlo Park, CA, USA (1999)
Björnsson, Y., Finnsson, H.: CadiaPlayer: A simulation-based General Game Player. IEEE Trans. Comput. Intell. AI Games 1(l), 4–15 (2009)
Bouzy, B., Helmstetter, B.: Monte-Carlo Go developments. In: van den Herik, H.J., Iida, H., Heinz, E.A. (eds.) Advances in Computer Games 10: Many Games, Many Challenges. IFIP Advances in Information and Communication Technology, vol. 135, pp. 159–174. Kluwer, Boston (2004)
Browne, C.B., Powley, E., Whitehouse, D., Lucas, S.M., Cowling, P.I., Rohlfshagen, P., Tavener, S., Perez, D., Samothrakis, S., Colton, S.: A survey of Monte Carlo Tree Search methods. IEEE Trans. Comput. Intell. AI Games 4(1), 1–43 (2012)
Cazenave, T., Saffidine, A.: Score bounded Monte-Carlo Tree Search. In: van den Herik, H.J., Iida, H., Plaat, A. (eds.) Computers and Games (CG 2010). Lecture Notes in Computer Science, vol. 6515, pp. 93–104. Springer, Berlin (2011)
Chaslot, G.M.J.-B., Winands, M.H.M., van den Herik, H.J.: Parallel Monte-Carlo Tree Search. In: van den Herik, H.J., Xu, X., Ma, Z., Winands, M.H.M. (eds.) Computers and Games (CG 2008). Lecture Notes in Computer Science, vol. 5131, pp. 60–71. Springer, Berlin (2008a)
Chaslot, G.M.J.-B., Winands, M.H.M., van den Herik, H.J., Uiterwijk, J.W.H.M., Bouzy, B.: Progressive strategies for Monte-Carlo Tree Search. New Math. Nat. Comput. 4(3), 343–357 (2008b)
Childs, B.E., Brodeur, J.H., Kocsis, L.: Transpositions and move groups in Monte Carlo Tree Search. In: Hingston, P., Barone, L. (eds.) Proceedings of the 2008 IEEE Symposium on Computational Intelligence and Games, pp. 389–395. IEEE, Piscataway, NJ, USA (2008)
Ciancarini, P., Favini, G.P.: Monte Carlo Tree Search in Kriegspiel. AI J. 174(11), 670–684 (2010)
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. (eds.) Computers and Games (CG 2006). Lecture Notes in Computer Science, vol. 4630, pp. 72–83. Springer, Berlin (2007)
Cowling, P.I., Powley, E.J., Whitehouse, D.: Information set Monte Carlo Tree Search. IEEE Trans. Comput. Intell. AI Games 4(2), 120–143 (2012)
Enzenberger, M., Müller, M.: A lock-free multithreaded Monte-Carlo Tree Search algorithm. In: van den Herik, H.J., Spronck, P. (eds.) Advances in Computer Games (ACG 2009). Lecture Notes in Computer Science (LNCS), vol. 6048, pp. 14–20. Springer, Berlin (2010)
Enzenberger, M., Müller, 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 Games 2(4), 259–270 (2010)
Gelly, S., Kocsis, L., Schoenauer, M., Sebag, M., Silver, D., Szepesvári, C., Teytaud, O.: The grand challenge of computer Go: Monte Carlo Tree Search and extensions. Commun. ACM 55(3), 106–113 (2012)
Ginsberg, M.L.: GIB: Steps toward an expert-level bridge-playing program. In: Dean, T. (ed.) Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence (IJCAI-99), vol. 1, pp. 584–589. Morgan Kaufmann, San Francisco, CA, USA (1999)
Hennes, D., Izzo, D.: Interplanetary trajectory planning with Monte Carlo Tree Search. In: Yang, Q., Wooldridge, M. (eds.) Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence (IJCAI 2015), pp. 769–775. AAAI Press, Menlo Park, CA, USA (2015)
Kocsis, L., Szepesvári, C.: Bandit based Monte-Carlo Planning. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) Machine Learning: ECML 2006. Lecture Notes in Artificial Intelligence, vol. 4212, pp. 282–293. Springer, Berlin (2006)
Lorentz, R.J.: Amazons discover Monte-Carlo. In: van den Herik, H.J., Xu, X., Ma, Z., Winands, M.H.M. (eds.) Computers and Games (CG 2008). Lecture Notes in Computer Science, vol. 5131, pp. 13–24. Springer, Berlin (2008)
Nguyen, K.Q., Thawonmas, R.: Monte Carlo Tree Search for collaboration control of Ghosts in Ms. Pac-Man. IEEE Trans. Comput. Intell. AI Games 5(1), 57–68 (2013)
Nijssen, J.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.) Computers and Games (CG 2010). Lecture Notes in Computer Science, vol. 6151, pp. 238–249. Springer, Berlin (2011)
Nijssen, J.A.M., Winands, M.H.M.: Monte Carlo Tree Search for the hide-and-seek game Scotland Yard. Trans. Comput. Intell. AI Games 4(4), 282–294 (2012)
Pepels, T., Winands, M.H.M., Lanctot, M.: Real-time Monte Carlo Tree Search in Ms Pac-Man. IEEE Trans. Comput. Intell. AI Games 6(3), 245–257 (2014)
Perez, D., Samothrakis, S., Lucas, S.M.: Knowledge-based fast evolutionary MCTS for general video game playing. In: Proceedings of the IEEE Conference on Computational Intelligence and Games (CIG 2014), pp. 68–75 (2014)
Ruijl, B., Vermaseren, J., Plaat, A. van den Herik, H.J.: Combining simulated annealing and Monte Carlo Tree Search for expression simplification. In: ICAART 2014, pp. 724–731 (2014)
Schadd, M.P.D., Winands, M.H.M., Tak, M.J.W., Uiterwijk, J.W.H.M.: Single-player Monte-Carlo Tree Search for SameGame. Knowl.-Based Syst. 34, 3–11 (2012)
Sheppard, B.: World-championship-caliber Scrabble. Artif. Intell. 134(1–2), 241–275 (2002)
Sturtevant, N.R.: An analysis of UCT in multi-player games. ICGA J. 31(4), 195–208 (2008)
Tak, M.J.W., Winands, M.H.M., Björnsson, Y.: N-Grams and the last-good-reply policy applied in general game playing. IEEE Trans. Comput. Intell. AI Games 4(2), 73–83 (2012)
Tesauro, G., Galperin, G.R.: On-line policy improvement using Monte-Carlo search. In: Mozer, M.C., Jordan, M.I., Petsche, T. (eds.) Advances in Neural Information Processing Systems, vol. 9, pp. 1068–1074. MIT Press, Cambridge, MA, USA (1997)
Winands, M.H.M., Björnsson, Y., Saito, J.-T.: Monte Carlo Tree Search in Lines of Action. IEEE Trans. Comput. Intell. AI Games 2(4), 239–250 (2010)
Zhu, G., Lizotte, D., Hoey, J.: Scalable approximate policies for Markov decision process models of hospital elective admissions. Artif. Intell. Med. 61(1), 21–34 (2014)
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Winands, M.H.M. (2015). Monte-Carlo Tree Search. In: Lee, N. (eds) Encyclopedia of Computer Graphics and Games. Springer, Cham. https://doi.org/10.1007/978-3-319-08234-9_12-1
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DOI: https://doi.org/10.1007/978-3-319-08234-9_12-1
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