# Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation

arXiv: https://arxiv.org/abs/2201.00508 · HTML: https://mlsanity.com/paper/2201.00508/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2022.

## Built on by (most cited first, 10 of 10)

- [Rank-based Decomposable Losses in Machine Learning: A Survey](https://mlsanity.com/paper/2207.08768/) (2022)
- [Efficient Algorithms for Empirical Group Distributionally Robust Optimization and Beyond](https://mlsanity.com/paper/2403.03562/) (2024)
- [Stochastic Optimization for Spectral Risk Measures](https://mlsanity.com/paper/2212.05149/) (2022)
- [A Model-Based Method for Minimizing CVaR and Beyond](https://mlsanity.com/paper/2305.17498/) (2023)
- [Evaluating Model Performance Under Worst-case Subpopulations](https://mlsanity.com/paper/2407.01316/) (2024)
- [Statistical and Computational Guarantees for Influence Diagnostics](https://mlsanity.com/paper/2212.04014/) (2022)
- [Fast Computation of Superquantile-Constrained Optimization Through Implicit Scenario Reduction](https://mlsanity.com/paper/2405.07965/) (2024)
- [Certifiably Robust Model Evaluation in Federated Learning under Meta-Distributional Shifts](https://mlsanity.com/paper/2410.20250/) (2024)
- [Statistical Robustness of Interval CVaR Based Regression Models under Perturbation and Contamination](https://mlsanity.com/paper/2601.11420/) (2026)
- [Wasserstein Distributionally Robust Risk-Sensitive Estimation via Conditional Value-at-Risk](https://mlsanity.com/paper/2604.18546/) (2026)

## Abstract (arXiv)

R. Tyrell Rockafellar and collaborators introduced, in a series of works, new regression modeling methods based on the notion of superquantile (or conditional value-at-risk). These methods have been influential in economics, finance, management science, and operations research in general. Recently, they have been the subject of a renewed interest in machine learning, to address issues of distributional robustness and fair allocation. In this paper, we review some of these new applications of the superquantile, with references to recent developments. These applications involve nonsmooth superquantile-based objective functions that admit explicit subgradient calculations. To make these superquantile-based functions amenable to the gradient-based algorithms popular in machine learning, we show how to smooth them by infimal convolution and describe numerical procedures to compute the gradients of the smooth approximations. We put the approach into perspective by comparing it to other smoothing techniques and by illustrating it on toy examples.