Unsupervised Learning of Echo State Networks: A Case Study in Artificial Embryogeny

Echo State Networks (ESN) have demonstrated their efficiencyin supervised learning of time series: a "reservoir" of neuronsprovide a set of dynamical systems that can be linearly combined tomatch the target dynamics, using a simple quadratic optimisation algorithmto tune the few free parameters. In an unsupervised learningcontext, however, another optimiser is needed. In this paper, an adaptive(1+1)-Evolution Strategy is used to optimise an ESN to tackle the"flag" problem, a classical benchmark from multi-cellular artificial embryogeny:the genotype is the cell controller of a Continuous CellularAutomata, and the phenotype, the image that corresponds to the fixed-point of the resulting dynamical system, must match a given 2D pattern.This approach is able to provide excellent results with few evaluations,and favourably compares to that using the NEAT algorithm (a state-of-the-art neuro-evolution method) to evolve the cell controllers. Somecharacteristics of the fitness landscape of the ESN-based method are alsoinvestigated.

[1]  Risto Miikkulainen,et al.  Incremental Evolution of Complex General Behavior , 1997, Adapt. Behav..

[2]  Marc Schoenauer,et al.  Robust multi-cellular developmental design , 2007, GECCO '07.

[3]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[4]  Dario Floreano,et al.  Neuroevolution with Analog Genetic Encoding , 2006, PPSN.

[5]  Phil Husbands,et al.  Better Living Through Chemistry: Evolving GasNets for Robot Control , 1998, Connect. Sci..

[6]  David E. Moriarty,et al.  Symbiotic Evolution of Neural Networks in Sequential Decision Tasks , 1997 .

[7]  James L. McClelland.  Explorations In Parallel Distributed Processing , 1988 .

[8]  Lawrence D. Jackel,et al.  Backpropagation Applied to Handwritten Zip Code Recognition , 1989, Neural Computation.

[9]  Riccardo Poli,et al.  Genetic and Evolutionary Computation – GECCO 2004 , 2004, Lecture Notes in Computer Science.

[10]  Teuvo Kohonen,et al.  Self-Organizing Maps , 2010 .

[11]  Nikolaus Hansen,et al.  A restart CMA evolution strategy with increasing population size , 2005, 2005 IEEE Congress on Evolutionary Computation.

[12]  Wolfgang Banzhaf,et al.  Advances in Artificial Life , 2003, Lecture Notes in Computer Science.

[13]  Peter J. Angeline,et al.  An evolutionary algorithm that constructs recurrent neural networks , 1994, IEEE Trans. Neural Networks.

[14]  Yann LeCun,et al.  Optimal Brain Damage , 1989, NIPS.

[15]  Barak A. Pearlmutter.  Gradient calculations for dynamic recurrent neural networks: a survey , 1995, IEEE Trans. Neural Networks.

[16]  Kenneth O. Stanley,et al.  NEAT Particles: Design, Representation, and Animation of Particle System Effects , 2007, 2007 IEEE Symposium on Computational Intelligence and Games.

[17]  Petros Koumoutsakos,et al.  Learning Probability Distributions in Continuous Evolutionary Algorithms - a Comparative Review , 2004, Nat. Comput..

[18]  W. Vent,et al.  Rechenberg, Ingo, Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb. Frommann‐Holzboog‐Verlag. Stuttgart 1973. Broschiert , 1975 .

[19]  Timur Ash,et al.  Dynamic node creation in backpropagation networks , 1989 .

[20]  Julian Francis Miller,et al.  Evolving a Self-Repairing, Self-Regulating, French Flag Organism , 2004, GECCO.

[21]  Diego Federici,et al.  Evolution and Development of a Multicellular Organism: Scalability, Resilience, and Neutral Complexification , 2006, Artificial Life.

[22]  Herbert Jaeger,et al.  The''echo state''approach to analysing and training recurrent neural networks , 2001 .

[23]  P. Werbos,et al.  Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences , 1974 .

[24]  B. Kermanshahi,et al.  Feedforward versus recurrent neural networks for forecasting monthly japanese yen exchange rates , 1996 .

[25]  Hans-Paul Schwefel,et al.  Evolution strategies – A comprehensive introduction , 2002, Natural Computing.

[26]  Wolfgang Banzhaf.  On the Dynamics of an Artificial Regulatory Network , 2003, ECAL.

[27]  Frédéric Gruau,et al.  Genetic Synthesis of Modular Neural Networks , 1993, ICGA.

[28]  Xin Yao,et al.  Evolving artificial neural networks , 1999, Proc. IEEE.

[29]  L. Darrell Whitley,et al.  Cellular Encoding Applied to Neurocontrol , 1995, ICGA.

[30]  Peter J. Bentley,et al.  Bias and scalability in evolutionary development , 2005, GECCO '05.

[31]  Christian Lebiere,et al.  The Cascade-Correlation Learning Architecture , 1989, NIPS.

[32]  Kenneth O. Stanley,et al.  A novel generative encoding for exploiting neural network sensor and output geometry , 2007, GECCO '07.

[33]  José Carlos Príncipe,et al.  Analysis and Design of Echo State Networks , 2007, Neural Computation.

[34]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[35]  Risto Miikkulainen,et al.  Evolving Neural Networks through Augmenting Topologies , 2002, Evolutionary Computation.

[36]  Yann LeCun,et al.  Learning processes in an asymmetric threshold network , 1986 .