# Optimizing Shortfall Risk Metric for Learning Regression Models

arXiv: https://arxiv.org/abs/2505.17777 · HTML: https://mlsanity.com/paper/2505.17777/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 23 May 2025.

## Builds on (most cited first, 8 of 8)

- [Learning with Average Top-k Loss](https://mlsanity.com/paper/1705.08826/) (2017)
- [Learning Bounds for Risk-sensitive Learning](https://mlsanity.com/paper/2006.08138/) (2020)
- [A Wasserstein distance approach for concentration of empirical risk estimates](https://mlsanity.com/paper/1902.10709/) (2019)
- [Consistent Multiclass Algorithms for Complex Metrics and Constraints](https://mlsanity.com/paper/2210.09695/) (2022)
- [Risk Measures and Upper Probabilities: Coherence and Stratification](https://mlsanity.com/paper/2206.03183/) (2022)
- [Spectral risk-based learning using unbounded losses](https://mlsanity.com/paper/2105.04816/) (2021)
- [Stochastic Optimization for Spectral Risk Measures](https://mlsanity.com/paper/2212.05149/) (2022)
- [Online Estimation and Optimization of Utility-Based Shortfall Risk](https://mlsanity.com/paper/2111.08805/) (2021)

## Abstract (arXiv)

We consider the problem of estimating and optimizing utility-based shortfall risk (UBSR) of a loss, say (Y - hat Y)2, in the context of a regression problem. Empirical risk minimization with a UBSR objective is challenging since UBSR is a non-linear function of the underlying distribution. We first derive a concentration bound for UBSR estimation using independent and identically distributed (i.i.d.) samples. We then frame the UBSR optimization problem as minimization of a pseudo-linear function in the space of achievable distributions mathcal D of the loss (Y- hat Y)2. We construct a gradient oracle for the UBSR objective and a linear minimization oracle (LMO) for the set mathcal D. Using these oracles, we devise a bisection-type algorithm, and establish convergence to the UBSR-optimal solution.