  Neuroevolution has yet to scale up to complex reinforcement learning tasks
that require large networks. Networks with many inputs (e.g. raw video) imply a
very high dimensional search space if encoded directly. Indirect methods use a
more compact genotype representation that is transformed into networks of
potentially arbitrary size. In this paper, we present an indirect method where
networks are encoded by a set of Fourier coefficients which are transformed
into network weight matrices via an inverse Fourier-type transform. Because
there often exist network solutions whose weight matrices contain regularity
(i.e. adjacent weights are correlated), the number of coefficients required to
represent these networks in the frequency domain is much smaller than the
number of weights (in the same way that natural images can be compressed by
ignore high-frequency components). This "compressed" encoding is compared to
the direct approach where search is conducted in the weight space on the
high-dimensional octopus arm task. The results show that representing networks
in the frequency domain can reduce the search-space dimensionality by as much
as two orders of magnitude, both accelerating convergence and yielding more
general solutions.
