Compressed Network Complexity Search
Indirect encoding schemes for neural network phenotypes can represent large networks compactly. In previous work, we presented a new approach where networks are encoded indirectly as a set of Fourier-type coefficients that decorrelate weight matrices such that they can often be represented by a small number of genes, effectively reducing the search space dimensionality, and speed up search. Up to now, the complexity of networks using this encoding was fixed a priori, both in terms of (1) the number of free parameters (topology) and (2) the number of coefficients. In this paper, we introduce a method, called Compressed Network Complexity Search (CNCS), for automatically determining network complexity that favors parsimonious solutions. CNCS maintains a probability distribution over complexity classes that it uses to select which class to optimize. Class probabilities are adapted based on their expected fitness. Starting with a prior biased toward the simplest networks, the distribution grows gradually until a solution is found. Experiments on two benchmark control problems, including a challenging non-linear version of the helicopter hovering task, demonstrate that the method consistently finds simple solutions.
KeywordsCompression Ratio Bias Weight Search Space Dimensionality Search Distribution Recurrent Weight
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- 1.Abbeel, P., Ganapathi, V., Ng, A.Y.: Learning vehicular dynamics, with application to modeling helicopters. In: NIPS (2005)Google Scholar
- 3.Gruau, F.: Cellular encoding of genetic neural networks. Technical Report RR-92-21, Ecole Normale Superieure de Lyon, Institut IMAG, Lyon, France (1992)Google Scholar
- 5.Koutník, J., Gomez, F., Schmidhuber, J.: Evolving neural networks in compressed weight space. In: Proceedings of the Conference on Genetic and Evolutionary Computation, GECCO 2010 (2010)Google Scholar
- 6.Koutník, J., Gomez, F., Schmidhuber, J.: Searching for minimal neural networks in fourier space. In: Proc. of the 4th Conf. on Artificial General Intelligence (2010)Google Scholar
- 7.Levin, L.A.: Universal sequential search problems. Problems of Information Transmission 9(3), 265–266 (1973)Google Scholar
- 12.Wierstra, D., Schaul, T., Peters, J., Schmidhuber, J.: Natural Evolution Strategies. In: Proceedings of the Congress on Evolutionary Computation (CEC 2008), Hongkong. IEEE Press (2008)Google Scholar
- 13.Wierstra, D., Schaul, T., Sun, T.G.Y., Schmidhuber, J.: Natural evolution strategies. Technical report (2011), arXiv:1106.4487v1Google Scholar
- 15.Zhang, B.-T., Muhlenbein, H.: Evolving optimal neural networks using genetic algorithms with Occam’s razor. Complex Systems 7, 199–220 (1993)Google Scholar