Recent advances in deep learning renewed the search for novel methods of deep neural network (DNN) optimization and training. Evolutionary algorithms (EA) applied directly to this problem have, so far, failed to demonstrate convincing advantages over gradient-based techniques. The approach proposed here labelled Deep Learning Evolution (DLE) overcomes the limitation of traditional genetic algorithms. This is possible due to the following feature: the training data themselves are treated as a genotype and are subject to crossovers and mutations, while DNN parameters and architecture are not modified by genetic operators directly. The method is empirically evaluated on a cooperative multiagent task. Results demonstrate consistent improvements over reinforcement and supervised learning. The paper presents theoretical foundations of the method, details of the algorithm, and results of its evaluation on a series of benchmark numerical experiments. The proposed approach has a potential to serve as a new general paradigm in constructing more versatile and adaptive neural systems applicable to a wide range of complex domains.