  Counterfactual Explanations (CEs) have received increasing interest as a
major methodology for explaining neural network classifiers. Usually, CEs for
an input-output pair are defined as data points with minimum distance to the
input that are classified with a different label than the output. To tackle the
established problem that CEs are easily invalidated when model parameters are
updated (e.g. retrained), studies have proposed ways to certify the robustness
of CEs under model parameter changes bounded by a norm ball. However, existing
methods targeting this form of robustness are not sound or complete, and they
may generate implausible CEs, i.e., outliers wrt the training dataset. In fact,
no existing method simultaneously optimises for closeness and plausibility
while preserving robustness guarantees. In this work, we propose Provably
RObust and PLAusible Counterfactual Explanations (PROPLACE), a method
leveraging on robust optimisation techniques to address the aforementioned
limitations in the literature. We formulate an iterative algorithm to compute
provably robust CEs and prove its convergence, soundness and completeness.
Through a comparative experiment involving six baselines, five of which target
robustness, we show that PROPLACE achieves state-of-the-art performances
against metrics on three evaluation aspects.
