  We consider the problem of learning classification trees that are robust to
distribution shifts between training and testing/deployment data. This problem
arises frequently in high stakes settings such as public health and social work
where data is often collected using self-reported surveys which are highly
sensitive to e.g., the framing of the questions, the time when and place where
the survey is conducted, and the level of comfort the interviewee has in
sharing information with the interviewer. We propose a method for learning
optimal robust classification trees based on mixed-integer robust optimization
technology. In particular, we demonstrate that the problem of learning an
optimal robust tree can be cast as a single-stage mixed-integer robust
optimization problem with a highly nonlinear and discontinuous objective. We
reformulate this problem equivalently as a two-stage linear robust optimization
problem for which we devise a tailored solution procedure based on constraint
generation. We evaluate the performance of our approach on numerous publicly
available datasets, and compare the performance to a regularized, non-robust
optimal tree. We show an increase of up to 12.48% in worst-case accuracy and of
up to 4.85% in average-case accuracy across several datasets and distribution
shifts from using our robust solution in comparison to the non-robust one.
