In this thesis, we assess a new framework called UMIN on a data-driven optimization problem. Such a problem happens recurrently in real life and can quickly become dicult to model when the input has a high dimensionality as images for instance. From the architecture of aircraft to the design of proteins, a great number of dierent techniques have already been explored. Based on former solutions, this work introduces a brand new Bayesian approach that updates previous frameworks. Former model architectures use generative adversarial networks on one side and a forward model on the other side to improve the accuracy of the results. However, employing a Bayesian network allows us to leverage its uncertainty estimates to enhance the accuracy of the results and also to reduce unrealistic samples output by the generator. By creating new experiments on a modern MNIST dataset and by reproducing former works taken as baseline, we show that the framework introduces in this work outperforms the previous method. The whole code is available at the following url: https://github.com/RomainGratier/Black-box_Optimization_via_Deep_ Generative-Exploratory_Networks.