  We consider the problem of learning an optimal prescriptive tree (i.e., an
interpretable treatment assignment policy in the form of a binary tree) of
moderate depth, from observational data. This problem arises in numerous
socially important domains such as public health and personalized medicine,
where interpretable and data-driven interventions are sought based on data
gathered in deployment -- through passive collection of data -- rather than
from randomized trials. We propose a method for learning optimal prescriptive
trees using mixed-integer optimization (MIO) technology. We show that under
mild conditions our method is asymptotically exact in the sense that it
converges to an optimal out-of-sample treatment assignment policy as the number
of historical data samples tends to infinity. Contrary to existing literature,
our approach: 1) does not require data to be randomized, 2) does not impose
stringent assumptions on the learned trees, and 3) has the ability to model
domain specific constraints. Through extensive computational experiments, we
demonstrate that our asymptotic guarantees translate to significant performance
improvements in finite samples, as well as showcase our uniquely flexible
modeling power by incorporating budget and fairness constraints.
