Machine learning (ML) and artificial intelligence (AI) have been rising themes of research for decades because they have been considered as one way to produce novel algorithms for solving striking challenges such as language understanding, best expert advice finding, automatic signal treatment, or financial fraud detection. The explosion of datascientist jobs is certainly an evidence of the societal, economic and scientific impact of ML. The fields of application of ML and AI have been rapidly growing, and these technologies are now crucial for decision making in many areas such as industry, banking, internet, bio-informatics or medical imaging (among many others) (see e.g. LeCun, Bengio and Hinton. Deep Learning. Nature, 2015). The cornerstone of ML methods is the intensive use of mathematics with a focus on tools from optimization and statistics. Indeed, ML generally involves the computation of hidden parameters for a system designed to make decisions based on yet unseen data for which optimization and statistics play a crucial role. However, for a long time, these two domains of applied mathematics were considered separately with little interactions.

Nevertheless, in the last decades, new ML problems have led to the evidence of the imperious necessity to mix the research fields of statistics and optimization as wells as  same theory to solve complex learning tasks due to the amount of a new data in the digital age. The combination of these research fields allow to handle both randomness and high dimensional features, the development of efficient numerical algorithms for recovering unknown parameters, and the understanding of worst case scenarios for robust learning or cooperative behaviour.