In evolutionary policy search, neural networks are usually represented using a direct mapping: each gene encodes one network weight. Indirect encoding methods, where each gene can encode for multiple weights, shorten the genome to reduce the dimensions of the search space and better exploit permutations and symmetries. The Geometric Encoding for Neural network Evolution (GENE) introduced an indirect encoding where the weight of a connection is computed as the (pseudo-)distance between the two linked neurons, leading to a genome size growing linearly with the number of genes instead of quadratically in direct encoding. However GENE still relies on hand-crafted distance functions with no prior optimization. Here we show that better performing distance functions can be found for GENE using Cartesian Genetic Programming (CGP) in a meta-evolution approach, hence optimizing the encoding to create a search space that is easier to exploit. We show that GENE with a learned function can outperform both direct encoding and the hand-crafted distances, generalizing on unseen problems, and we study how the encoding impacts neural network properties.

翻译：在进化策略搜索中，神经网络通常使用直接映射表示：每个基因编码一个网络权重。间接编码方法中，每个基因可以编码多个权重，从而缩短基因组以降低搜索空间的维度，并更好地利用排列和对称性。用于神经进化几何编码（GENE）引入了一种间接编码，其中连接的权重通过两个相连神经元之间的（伪）距离计算，使得基因组大小随基因数量线性增长，而非直接编码中的二次增长。然而，GENE仍依赖于手工设计的距离函数，且未进行先验优化。在此，我们展示通过使用笛卡尔遗传编程（CGP）进行元进化方法，可以为GENE找到性能更优的距离函数，从而优化编码以创造更易于利用的搜索空间。我们证明，带有学习函数的GENE在性能上可以超越直接编码和手工设计的距离，并在未见问题上展现出泛化能力；同时，我们研究了编码对神经网络性质的影响。