# From Data to Uncertainty Sets: a Machine Learning Approach

arXiv: https://arxiv.org/abs/2503.02173 · HTML: https://mlsanity.com/paper/2503.02173/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 25 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 6 of 6)

- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [An Overview of Multi-Task Learning in Deep Neural Networks](https://mlsanity.com/paper/1706.05098/) (2017)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Reliable training and estimation of variance networks](https://mlsanity.com/paper/1906.03260/) (2019)
- [Predict-then-Calibrate: A New Perspective of Robust Contextual LP](https://mlsanity.com/paper/2305.15686/) (2023)

## Abstract (arXiv)

Existing approaches of prescriptive analytics -- where inputs of an optimization model can be predicted by leveraging covariates in a machine learning model -- often attempt to optimize the mean value of an uncertain objective. However, when applied to uncertain constraints, these methods rarely work because satisfying a crucial constraint in expectation may result in a high probability of violation. To remedy this, we leverage robust optimization to protect a constraint against the uncertainty of a machine learning model's output. To do so, we design an uncertainty set based on the model's loss function. Intuitively, this approach attempts to minimize the uncertainty around a prediction. Extending guarantees from the robust optimization literature, we derive strong guarantees on the probability of violation. On synthetic computational experiments, our method requires uncertainty sets with radii up to one order of magnitude smaller than those of other approaches.