  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 regression method by proposing
a first-order optimization algorithm to minimize a superquantile-based learning
objective. The proposed algorithm is based on smoothing the superquantile
function by infimal convolution. Promising numerical results illustrate the
interest of the approach towards safer supervised learning.
