Abstract: Counterfactual (CF) explanations for machine learning (ML) models are preferred by end-users, as they explain the predictions of ML models by providing a recourse case to individuals who are adversely impacted by predicted outcomes. Existing CF explanation methods generate recourses under the assumption that the underlying target ML model remains stationary over time. However, due to commonly occurring distributional shifts in training data, ML models constantly get updated in practice, which might render previously generated recourses invalid and diminish end-users trust in our algorithmic framework. To address this problem, we propose RoCourseNet, a training framework that jointly optimizes for predictions and robust recourses to future data shifts. We have three main contributions: (i) We propose a novel \emph{virtual data shift (VDS)} algorithm to find worst-case shifted ML models by explicitly considering the worst-case data shift in the training dataset. (ii) We leverage adversarial training to solve a novel tri-level optimization problem inside RoCourseNet, which simultaneously generates predictions and corresponding robust recourses. (iii) Finally, we evaluate RoCourseNet's performance on three real-world datasets and show that RoCourseNet outperforms state-of-the-art baselines by $\sim$10\% in generating robust CF explanations.