First-order Optimization for Superquantile-based Supervised Learning

TL;DR

This paper introduces a first-order optimization algorithm for superquantile regression, enhancing the robustness of supervised learning models against distribution shifts between training and testing data.

Contribution

It proposes a novel smoothing-based first-order optimization method for superquantile-based learning objectives, improving safety and robustness in supervised learning.

Findings

Numerical results demonstrate the effectiveness of the proposed approach.

The method enhances model safety under distributional shifts.

Abstract

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.