Abstract
In the last decade, proof-number search and Monte-Carlo methods have successfully been applied to the combinatorial-games domain. Proof-number search is a reliable algorithm. It requires a well defined goal to prove. This can be seen as a disadvantage. In contrast to proof-number search, Monte-Carlo evaluation is a flexible stochastic evaluation for game-tree search. In order to improve the efficiency of proof-number search, we introduce a new algorithm, Monte-Carlo Proof-Number search. It enhances proof-number search by adding the flexible Monte-Carlo evaluation. We present the new algorithm and evaluate it on a sub-problem of Go, the Life-and-Death problem. The results show a clear improvement in time efficiency and memory usage: the test problems are solved two times faster and four times less nodes are expanded on average. Future work will assess possibilities to extend this method to other enhanced Proof-Number techniques.
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References
Allis, L.V., van der Meulen, M., van den Herik, H.J.: Proof-Number Search. Artificial Intelligence 66, 91–124 (1994)
Bouzy, B., Helmstetter, B.: Monte Carlo Developments. In: van den Herik, H.J., Iida, H., Heinz, E.A. (eds.) 10th Advances in Computer Games (ACG10), Many Games, Many Challenges, pp. 159–174. Kluwer Academic Publishers, Dordrecht (2004)
Bouzy, B.: Associating Shallow and Selective Global Tree Search with Monte Carlo for 9×9 Go. In: van den Herik, H.J., Björnsson, Y., Netanyahu, N.S. (eds.) CG 2004. LNCS, vol. 3846, pp. 76–80. Springer, Heidelberg (2006)
Bouzy, B.: History and Territory Heuristics for Monte-Carlo Go. In: Chen, K., et al. (eds.) Joint Conference on Information Sciences JCIS 2005, p. 4 (2005)
Breuker, D.M.: Memory versus Search. PhD thesis, Maastricht University (1998)
Brügmann, B.: Monte Carlo Go. White paper (1993)
Cazenave, T., Helmstetter, B.: Search for Transitive Connection. Information Sciences 132(1), 93–103 (2004)
Kishimoto, A.: Correct and Efficient Search Algorithms in the Presence of Repetitions. PhD thesis, University of Alberta (2005)
Kishimoto, A., Müller, M.: DF-PN in Go: Application to the One-Eye Problem. In: van den Herik, H.J., Iida, H., Heinz, E.A. (eds.) 10th Advances in Computer Games (ACG10), Many Games, Many Challenges, pp. 125–141. Kluwer Academic Publishers, Dordrecht (2003)
Nagai, A.: Df-pn Algorithm for Searching AND/OR Trees and Its Applications. PhD thesis, University of Tokio (2002)
Schaeffer, J., Björnsson, Y., Burch, N., Kishimoto, A., Muller, M., Lake, R., Lu, P., Sutphen, S.: Solving Checkers. In: International Joint Conference on Artificial Intelligence (IJCAI), pp. 292–297 (2005)
Seo, M., Iida, H., Uiterwijk, J.W.H.M.: The PN*-Search Algorithm: Application to Tsume-Shogi. Artificial Intelligence 129(1-2), 253–277 (2001)
Sheppard, B.: Efficient Control of Selective Simulations. ICGA Journal 27(3), 67–80 (2005)
van der Steen, J.: GoBase.org website (2006), http://www.gobase.org
Winands, M.H.M., Uiterwijk, J.W.H.M., van den Herik, H.J.: An Effective Two-Level Proof-Number Search Algorithm. Theoretical Computer Science 313(3), 511–525 (2004)
Wolf, Th.: Forward Pruning and Other Heuristic Search Techniques in Tsume Go. Information Sciences 122(1), 59–76 (2000)
Zobrist, A.L.: A New Hashing Method with Application for Game Playing. ICCA Journal 13(2), 69–73 (1990)
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Saito, JT., Chaslot, G., Uiterwijk, J.W.H.M., van den Herik, H.J. (2007). Monte-Carlo Proof-Number Search for Computer Go. 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. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75538-8_5
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DOI: https://doi.org/10.1007/978-3-540-75538-8_5
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