In statistical learning, the distribution of the data can change between training and practical use-cases due to biases or distribution shifts. A remedy for this obstacle is to train a model on the worst distribution for the objective that is close to the data (in the sense of the Wasserstein distance). As this problem is often intractable, we first show how to regularize it in order to implement numerical methods, while controlling this approximation. Finally, we will also consider the statistical guarantees of such models. In collaboration with Waïss Azizian and Jérôme Malick.