  Recent development in the data-driven decision science has seen great
advances in individualized decision making. Given data with individual
covariates, treatment assignments and outcomes, policy makers best
individualized treatment rule (ITR) that maximizes the expected outcome, known
as the value function. Many existing methods assume that the training and
testing distributions are the same. However, the estimated optimal ITR may have
poor generalizability when the training and testing distributions are not
identical. In this paper, we consider the problem of finding an optimal ITR
from a restricted ITR class where there is some unknown covariate changes
between the training and testing distributions. We propose a novel
distributionally robust ITR (DR-ITR) framework that maximizes the worst-case
value function across the values under a set of underlying distributions that
are "close" to the training distribution. The resulting DR-ITR can guarantee
the performance among all such distributions reasonably well. We further
propose a calibrating procedure that tunes the DR-ITR adaptively to a small
amount of calibration data from a target population. In this way, the
calibrated DR-ITR can be shown to enjoy better generalizability than the
standard ITR based on our numerical studies.
