The objective of this project is to audit machine learning algorithms and make them compliant. The new legislation (RGPD and European Act) provides a legal framework that will frame the practical implementation of algorithms. They provide a number of recommendations that algorithms must follow. In particular, these algorithms must not behave differently for sub-groups of users unless these sub-groups are identified in advance and the differences are justified. They should also clearly display what they are designed to do and not mislead users. A large body of research exists to assess bias in machine learning as well as to study the explainability of algorithmic decisions. In the first place, this work should be pursued in order to better understand these problems and to develop procedures to certify the presence or absence of bias. In addition, the difficulty of auditing algorithms comes essentially from the fact that the measurements depend on the distribution of the sample. But in a "black box" auditing framework, i.e. knowing only the outputs of the algorithm on a data set previously selected or chosen by the auditor, it is necessary to take into account the variability of the algorithm with respect to the distributions themselves. Our objective in this project is therefore to develop new ways of defining, detecting and controlling the effects of biases, in a uniform and robust way when the distribution of the observations is partially known. Our approach is multi-disciplinary, relying on robust statistics and machine learning (maths and computer science) to define valid properties for distributional neighbourhoods, Gaussian processes for the construction of optimal experimental designs for the discovery of observations, and optimisation to be able to build algorithms practically.