Unsupervised Learning of Echo State Networks: A Case Study in Artificial Embryogeny
Echo State Networks (ESN) have demonstrated their efficiency in supervised learning of time series: a "reservoir" of neurons provide a set of dynamical systems that can be linearly combined to match the target dynamics, using a simple quadratic optimisation algorithm to tune the few free parameters. In an unsupervised learning context, however, another optimiser is needed. In this paper, an adaptive (1+1)-Evolution Strategy as well as the state-of-the-art CMA-ES are 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 Cellular Automata, 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. Some characteristics of the fitness landscape of the ESN-based method are also investigated.