  Algorithmic recourse recommends a cost-efficient action to a subject to
reverse an unfavorable machine learning classification decision. Most existing
methods in the literature generate recourse under the assumption of complete
knowledge about the cost function. In real-world practice, subjects could have
distinct preferences, leading to incomplete information about the underlying
cost function of the subject. This paper proposes a two-step approach
integrating preference learning into the recourse generation problem. In the
first step, we design a question-answering framework to refine the confidence
set of the Mahalanobis matrix cost of the subject sequentially. Then, we
generate recourse by utilizing two methods: gradient-based and graph-based
cost-adaptive recourse that ensures validity while considering the whole
confidence set of the cost matrix. The numerical evaluation demonstrates the
benefits of our approach over state-of-the-art baselines in delivering
cost-efficient recourse recommendations.
