# First-order Optimization for Superquantile-based Supervised Learning

arXiv: https://arxiv.org/abs/2009.14575 · HTML: https://mlsanity.com/paper/2009.14575/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2020.

## Built on by (most cited first, 4 of 4)

- [Exact Generalization Guarantees for (Regularized) Wasserstein Distributionally Robust Models](https://mlsanity.com/paper/2305.17076/) (2023)
- [Stochastic Optimization for Spectral Risk Measures](https://mlsanity.com/paper/2212.05149/) (2022)
- [Evaluating Model Performance Under Worst-case Subpopulations](https://mlsanity.com/paper/2407.01316/) (2024)
- [Federated Learning with Superquantile Aggregation for Heterogeneous Data](https://mlsanity.com/paper/2112.09429/) (2021)

## Abstract (arXiv)

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.