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.