First-order optimization for superquantile-based supervised learning

Classical supervised learning via empirical risk (or negative log-likelihood) minimization hinges upon the assumption that the testing distribution coincides with the training distribution. This assumption can be challenged in modern applications of machine learning in which learning machines may operate at prediction time with testing data whose distribution departs from the one of the training data. We revisit the superquantile approach proposed by Rockafellar and present a first-order optimization algorithm based on smoothing by infimal convolution to minimize a superquantile-based objective for safer supervised learning. Promising numerical results illustrate the interest of the approach.