# A Brief Introduction to Robust Bilevel Optimization

arXiv: https://arxiv.org/abs/2211.16072 · HTML: https://mlsanity.com/paper/2211.16072/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Nov 2022.

## Built on by (most cited first, 1 of 1)

- [Calibration in One Go: Jointly Learning Accurate and Calibrated Neural Networks](https://mlsanity.com/paper/2610.13693/) (2026)

## Abstract (arXiv)

Bilevel optimization is a powerful tool for modeling hierarchical decision making processes. However, the resulting problems are challenging to solve - both in theory and practice. Fortunately, there have been significant algorithmic advances in the field so that we can solve much larger and also more complicated problems today compared to what was possible to solve two decades ago. This results in more and more challenging bilevel problems that researchers try to solve today. In this article, we give a brief introduction to one of these more challenging classes of bilevel problems: bilevel optimization under uncertainty using robust optimization techniques. To this end, we briefly state different versions of uncertain bilevel problems that result from different levels of cooperation of the follower as well as on when the uncertainty is revealed. We highlight these concepts using an academic example and discuss recent results from the literature concerning complexity as well as solution approaches. Finally, we discuss that the sources of uncertainty in bilevel optimization are much richer than in single-level optimization and, to this end, introduce the concept of decision uncertainty.