Benchmarking Bilevel Derivative-Free Optimization Algorithms
Abstract
Bilevel optimization involves an upper-level and a lower-level decision maker. The lower-level optimization problem is nested within the constraints of the upper-level one. A point is said to be admissible for the bilevel problem if it satisfies all constraints and is optimal for the lower-level decision-maker. Bilevel derivative-free optimization (BL-DFO) algorithms address bilevel optimization problems in which the upper-level is solved using a derivative-free optimization method, and an inexact method it used to solve the lower- level. In this context, existing BL-DFO benchmarking techniques often do not rigorously validate the admissibility of proposed solutions, and do not adequately account for the computational effort deployed by the upper- and lower-level solvers. This work proposes a benchmarking methodology for BL-DFO algorithms. A post-optimization procedure, named the refereeing procedure, is introduced to discard non-admissible points and ensures a fair comparison between the algorithms. The computational effort deployed by upper- and lower-level solvers is also taken into account into the overall computational cost. Numerical experiments illustrate the benchmarking methodology.
Related
- Decision-focused predictions via pessimistic bilevel optimization: complexity and algorithms
- Single-Loop Gradient Algorithms for Pessimistic Bilevel Optimization Problems
- Efficient Hessian-Free Methods for Multi-Objective Bilevel Optimization with Nonconvex Lower Level
- A note on the complexity of random subspace model-based methods for derivative-free optimization
- Powell-Style Model-Based Derivative-Free Optimization with Complexity Guarantees
BibTeX
@misc{audet2026benchmarking,
title = {{Benchmarking Bilevel Derivative-Free Optimization Algorithms}},
author = {Charles Audet and Valentin Dijon and Youssef Diouane},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.30531},
eprint = {2605.30531},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.30531},
}
RIS
TY - UNPB
TI - Benchmarking Bilevel Derivative-Free Optimization Algorithms
AU - Charles Audet
AU - Valentin Dijon
AU - Youssef Diouane
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2605.30531
UR - https://arxiv.org/abs/2605.30531
AB - Bilevel optimization involves an upper-level and a lower-level decision maker. The lower-level optimization problem is nested within the constraints of the upper-level one. A point is said to be admissible for the bilevel problem if it satisfies all constraints and is optimal for the lower-level decision-maker. Bilevel derivative-free optimization (BL-DFO) algorithms address bilevel optimization problems in which the upper-level is solved using a derivative-free optimization method, and an inexact method it used to solve the lower- level. In this context, existing BL-DFO benchmarking techniques often do not rigorously validate the admissibility of proposed solutions, and do not adequately account for the computational effort deployed by the upper- and lower-level solvers. This work proposes a benchmarking methodology for BL-DFO algorithms. A post-optimization procedure, named the refereeing procedure, is introduced to discard non-admissible points and ensures a fair comparison between the algorithms. The computational effort deployed by upper- and lower-level solvers is also taken into account into the overall computational cost. Numerical experiments illustrate the benchmarking methodology.
ER -