Abstract
Learning to solve small instances of a problem should help in solving large instances. Unfortunately, most neural network architectures do not exhibit this form of scalability. Our Multi-Dimensional Recurrent LSTM Networks, however, show a high degree of scalability, as we empirically show in the domain of flexible-size board games. This allows them to be trained from scratch up to the level of human beginners, without using domain knowledge.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
van der Werf, E., van den Herik, H.J., Uiterwijk, J.: Solving Go on small boards. International Computer Games Association Journal 26 (2003)
Richards, N., Moriarty, D.E., Miikkulainen, R.: Evolving neural networks to play Go. Applied Intelligence 8, 85–96 (1997)
Runarsson, T.P., Lucas, S.M.: Co-evolution versus Self-play Temporal Difference Learning for Acquiring Position Evaluation in Small-board Go. IEEE Transactions on Evolutionary Computation, 628–640 (2005)
Wu, L., Baldi, P.: A Scalable Machine Learning Approach to Go. In: Schölkopf, B., Platt, J., Hoffman, T. (eds.) Advances in Neural Information Processing Systems 19, pp. 1521–1528. MIT Press, Cambridge (2007)
Stanley, K.O., Miikkulainen, R.: Evolving a Roving Eye for Go. In: Deb, K., et al. (eds.) GECCO 2004. LNCS, vol. 3103, pp. 1226–1238. Springer, Heidelberg (2004)
Schaul, T., Schmidhuber, J.: A Scalable Neural Network Architecture for Board Games. In: Proceedings of the IEEE Symposium on Computational Intelligence in Games. IEEE Press, Los Alamitos (2008)
Grüttner, M.: Evolving Multidimensional Recurrent Neural Networks for the Capture Game in Go. Bachelor Thesis, Techniche Universität München (2008)
Graves, A., Fernández, S., Schmidhuber, J.: Multidimensional Recurrent Neural Networks. In: Proceedings of the 2007 International Conference on Artificial Neural Networks (September 2007)
Graves, A.: Supervised Sequence Labelling with Recurrent Neural Networks, Ph.D. in Informatics, Fakultat für Informatik – Technische Universität München (2008)
Silver, D., Sutton, R.S., Müller, M.: Reinforcement Learning of Local Shape in the Game of Go. In: IJCAI, pp. 1053–1058 (2007)
Lecun, Y., Bengio, Y.: Convolutional Networks for Images, Speech and Time Series, pp. 255–258. The MIT Press, Cambridge (1995)
Schraudolph, N.N., Dayan, P., Sejnowski, T.J.: Temporal Difference Learning of Position Evaluation in the Game of Go. In: Cowan, J.D., Tesauro, G., Alspector, J. (eds.) Advances in Neural Information Processing Systems, vol. 6, pp. 817–824. Morgan Kaufmann, San Francisco (1994)
Freisleben, B., Luttermann, H.: Learning to Play the Game of Go-Moku: A Neural Network Approach. Australian Journal of Intelligent Information Processing Systems 3(2), 52–60 (1996)
Gauci, J., Stanley, K.: Generating large-scale neural networks through discovering geometric regularities. In: GECCO 2007: Proceedings of the 9th annual conference on Genetic and evolutionary computation, pp. 997–1004 (2007)
Schuster, M., Paliwal, K.K.: Bidirectional recurrent neural networks. IEEE Transactions on Signal Processing 45, 2673–2681 (1997)
Baldi, P., Pollastri, G.: The principled design of large-scale recursive neural network architectures DAG-RNNs and the protein structure prediction problem. Journal of Machine Learning Research 4, 575–602 (2003)
Graves, A., Schmidhuber, J.: Offline Handwriting Recognition with Multidimensional Recurrent Neural Networks. In: NIPS (2008)
Hochreiter, S., Schmidhuber, J.: Long short-term memory. Neural Computation 9(9), 1735–1780 (1997)
Gherman, S.: Atari-Go Applet (2000), http://www.361points.com/capturego/
Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation 9(2), 159–195 (2001)
Gomez, F., Miikkulainen, R.: Incremental Evolution of Complex General Behavior. Adaptive Behavior 5, 317–342 (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schaul, T., Schmidhuber, J. (2009). Scalable Neural Networks for Board Games. In: Alippi, C., Polycarpou, M., Panayiotou, C., Ellinas, G. (eds) Artificial Neural Networks – ICANN 2009. ICANN 2009. Lecture Notes in Computer Science, vol 5768. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04274-4_103
Download citation
DOI: https://doi.org/10.1007/978-3-642-04274-4_103
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04273-7
Online ISBN: 978-3-642-04274-4
eBook Packages: Computer ScienceComputer Science (R0)