Abstract
Monte-Carlo Tree Search (MCTS) is currently the dominant algorithm in Computer Go. MCTS is an asymmetric tree search technique employing stochastic simulations to evaluate leaves and guide the search. Using features to further guide MCTS is a powerful approach to improving performance. In Computer Go, these features are typically comprised of a number of hand-crafted heuristics and a collection of patterns, with weights for these features usually trained using data from high-level Go games. This paper investigates the feasibility of using decision trees to generate features for Computer Go. Our experiments show that while this approach exhibits potential, our initial prototype is not as powerful as using traditional pattern features.
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- 1.
This graph representation was chosen in the view that it may improve the opening of Oakfoam, the MCTS implementation being extended [14].
- 2.
A variation of pseudo-liberties [15] (where chains in atari have their number of pseudo-liberties set to one) was used to simplify implementation.
- 3.
This parameter can be any combination of black, white and side, such as: black or side.
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[x|y] means either x or y.
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This is designed to deal with NEW queries that have more than two children.
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However, we later discovered that the MM tool was unable to deal with large training data sets for our tests.
- 7.
Note that this violates the conceptual view that the decision tree partitions the input space, since one position may ultimately correspond to multiple leaf nodes.
References
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Acknowledgments
The first author would like to thank the MIH Media Lab at Stellenbosch University for the use of their facilities and support of the work presented here.
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Appendices
Multiple Decision Tree Descent Paths
It is possible that a NEW decision tree query may not be able to identify a unique node from the ASG to add to the discovered graph. In this situation, a sequence of conditions are considered, in an attempt to enforce uniqueness. Each condition will select the node(s) that best satisfy the condition and eliminate the others. These conditions are designed to enforce invariance to changes in rotation and reflection as far as possible. If the conditions are not able to identify a unique node, then each of the possibilities is considered.Footnote 7 The sequence of conditions used in this work is as follows:
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Select node(s) closest to the candidate move.
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Select black over white over side nodes.
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Select node(s) closest to nodes already in the discovered graph, in reverse order of discovery.
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Select node(s) with the most stones in its respective chain.
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Select node(s) with the most liberties around its respective chain.
Even though these conditions are not always able to find a unique node, empirical results showed that a single leaf node is reached in about 85 % of tree descents. It was therefore decided to only return one of these nodes, namely the left-most node in the tree. Investigation showed that this option made negligible difference to move prediction accuracy, while providing a large reduction in training time and an increase in the size of training data set that could be handled. This is due to the leaf nodes of each decision tree becoming mutually exclusive, allowing decision trees to be treated as single features.
Reproducibility
All source code used in this work is available in the codebase of Oakfoam, an open-source MCTS-based Computer Go player [14]. Version 0.1.3 was used for the work in this paper and is tagged in the code repository. Default parameters were used unless specified otherwise.
The MM tool of Rémi Coulom was used to train feature weights. This tool is available at: http://remi.coulom.free.fr/Amsterdam2007/.
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van Niekerk, F., Kroon, S. (2014). Decision Trees for Computer Go Features. In: Cazenave, T., Winands, M., Iida, H. (eds) Computer Games. CGW 2013. Communications in Computer and Information Science, vol 408. Springer, Cham. https://doi.org/10.1007/978-3-319-05428-5_4
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