# Bayesian Optimization of Bilevel Problems

arXiv: https://arxiv.org/abs/2412.18518 · HTML: https://mlsanity.com/paper/2412.18518/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2024.

## Built on by (most cited first, 3 of 3)

- [BILBO: BILevel Bayesian Optimization](https://mlsanity.com/paper/2502.02121/) (2025)
- [Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems](https://mlsanity.com/paper/2509.21725/) (2025)
- [Exploiting Separability in Multi-Scale Grey-Box Bayesian Optimization](https://mlsanity.com/paper/2608.03045/) (2026)

## Abstract (arXiv)

Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics, engineering, and machine learning. This paper focuses on bilevel optimization where both upper-level and lower-level functions are black boxes and expensive to evaluate. We propose a Bayesian Optimization framework that models the upper and lower-level functions as Gaussian processes over the combined space of upper and lower-level decisions, allowing us to exploit knowledge transfer between different sub-problems. Additionally, we propose a novel acquisition function for this model. Our experimental results demonstrate that the proposed algorithm is highly sample-efficient and outperforms existing methods in finding high-quality solutions.