We recently published our new paper titled “A wavelet-based Encoding for Neuroevolution” in the Proceedings of the 2016 Genetic and Evolutionary Computation Conference (GECCO).
In our paper we introduce a novel indirect encoding scheme that encodes neural network connection weights as low-frequency wavelet-domain coefficients. A lossy Discrete Inverse Wavelet Transform (IDWT) maps these coefficients back to the neural network phenotype. This Wavelet-based Encoding (WBE) builds on top of a Discrete Cosine Transform (DCT) encoding  and similarly satisfies continuity in the genotype-phenotype mapping. However, unlike the DCT encoding, the WBE satisfies a variable degree of gene-locality.
In our experiments we observe that the WBE yields superior performance on the Octopus-arm Control task (a relevant benchmark used previously for a Reinforcement Learning competition) compared to the DCT encoding. We argue that this is due to the added gene-locality of the WBE, which positively affects the efficiency of training neural networks by means of evolutionary search. A more general theoretically motivated intuition underlying our reasoning is presented in the paper.
Other novelties in our approach arise from the flexibility of the WBE. Being able to freely choose the wavelet basis function to compute the IDWT we were able to augment the WBE with a dynamic basis function, which can be optimised alongside the low-frequency wavelet coefficients by means of the same evolutionary algorithm. The resulting approach is able to optimise the mapping and coefficients simultaneously.
 Koutnik, Jan, Faustino Gomez, and Jürgen Schmidhuber. “Evolving neural networks in compressed weight space.” Proceedings of the 12th annual conference on Genetic and evolutionary computation. ACM, 2010.