## Efficient selectivity and backup operators in Monte-Carlo tree search (2006)

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Venue: | In: Proceedings Computers and Games 2006 |

Citations: | 124 - 2 self |

### BibTeX

@INPROCEEDINGS{Coulom06efficientselectivity,

author = {Rémi Coulom},

title = {Efficient selectivity and backup operators in Monte-Carlo tree search},

booktitle = {In: Proceedings Computers and Games 2006},

year = {2006},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

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### Abstract

Abstract. Monte-Carlo evaluation consists in estimating a position by averaging the outcome of several random continuations, and can serve as an evaluation function at the leaves of a min-max tree. This paper presents a new framework to combine tree search with Monte-Carlo evaluation, that does not separate between a min-max phase and a Monte-Carlo phase. Instead of backing-up the min-max value close to the root, and the average value at some depth, a more general backup operator is defined that progressively changes from averaging to min-max as the number of simulations grows. This approach provides a fine-grained control of the tree growth, at the level of individual simulations, and allows efficient selectivity methods. This algorithm was implemented in a 9 × 9 Go-playing program, Crazy Stone, that won the 10th KGS computer-Go tournament. 1

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4081 | Reinforcement Learning: An Introduction
- Sutton, Barto
- 1998
(Show Context)
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1299 | Learning to predict by the methods of temporal differences
- Sutton
- 1988
(Show Context)
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275 |
An analysis of alpha-beta pruning
- Knuth, Moore
- 1975
(Show Context)
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- Kearns, Mansour, et al.
- 2002
(Show Context)
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- Ginsberg
- 1999
(Show Context)
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71 | Searching for Solutions in Games and Artificial Intelligence
- Allis
- 1994
(Show Context)
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63 | Simulation budget allocation for further enhancing the efficiency of ordinal optimization. Discrete Event Dynamic Systems: Theory
- Chen, Lin, et al.
- 2000
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45 |
Searching with Probabilities
- Palay
- 1983
(Show Context)
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- Tesauro
- 2002
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Expected-outcome: a general model of static evaluation
- Abramson
- 1990
(Show Context)
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- Baum, Smith
- 1997
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Monte Carlo Go developments
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- Enzenberger
- 2003
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On-line search for solving large Markov decision processes
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- 1999
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Computer Go tournaments on KGS. http://www.weddslist.com/ kgs/, 2005. A Random Simulations in Crazy Stone The most basic method to perform random simulations in computer-Go consists in selecting legal moves uniformly at random, with the exception of eye-f
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