Work

Computing weak counterfactual explanations for linear optimization: A new class of bilevel models and a tailored penalty alternating direction method

Year: 2026

Type: article

Abstract: In recent years, significant attention has been devoted to the issue of explainability in automated decision-making tools. The idea is to explain the outcome of a model by presenting a certain change in the input of the model so that the outcome changes significantly. In this paper, we study this question for linear optimization problems as an automated decision-making tool. This leads to a new class of linear bilevel optimization problems that have more nonlinearities in their single-level reformulations compared to traditionally studied linear bilevel problems. For this class of problems, we present a tailored penalty alternating direction method and present its convergence theory that mainly ensures that we compute stationary points of the single-level reformulation. Finally, we illustrate the applicability of this method using the example of a real-world energy system model as well as by computing counterfactual explanations for a large set of linear optimization problems from the NETLIB as it has been proposed in the recent literature.

Source: European Journal of Operational Research

DOI: 10.1016/j.ejor.2026.02.007

Authors: Henri Lefebvre, Martin Schmidt

Institutions: Centre National de la Recherche Scientifique, Université de Montpellier, Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier, Universität Trier

Language: English

Topic: Explainable Artificial Intelligence (XAI)

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Deutsche Forschungsgemeinschaft, Bundesministerium für Bildung und Forschung