First-order Optimization for Superquantile-based Supervised Learning

Yassine Laguel (1) , Jérôme Malick (1) , Zaid Harchaoui (2)

1 DAO - Données, Apprentissage et Optimisation
2 University of Washington [Seattle]

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.

Mots clés: supervised learning; risk measure; distributional robustness; nonsmooth optimization

Domaines: Optimisation et contrôle [math.OC]; Statistiques [stat]; Apprentissage [cs.LG]

Yassine Laguel, Jérôme Malick, Zaid Harchaoui. First-order Optimization for Superquantile-based Supervised Learning. IEEE International Workshop on Machine Learning for Signal Processing, Sep 2020, Espoo, Finland. ⟨10.1109/MLSP49062.2020.9231909⟩. ⟨hal-02953846⟩