  Counterfactual explanations play an important role in detecting bias and
improving the explainability of data-driven classification models. A
counterfactual explanation (CE) is a minimal perturbed data point for which the
decision of the model changes. Most of the existing methods can only provide
one CE, which may not be achievable for the user. In this work we derive an
iterative method to calculate robust CEs, i.e. CEs that remain valid even after
the features are slightly perturbed. To this end, our method provides a whole
region of CEs allowing the user to choose a suitable recourse to obtain a
desired outcome. We use algorithmic ideas from robust optimization and prove
convergence results for the most common machine learning methods including
logistic regression, decision trees, random forests, and neural networks. Our
experiments show that our method can efficiently generate globally optimal
robust CEs for a variety of common data sets and classification models.
