  We study the problem of learning individualized dose intervals using
observational data. There are very few previous works for policy learning with
continuous treatment, and all of them focused on recommending an optimal dose
rather than an optimal dose interval. In this paper, we propose a new method to
estimate such an optimal dose interval, named probability dose interval (PDI).
The potential outcomes for doses in the PDI are guaranteed better than a
pre-specified threshold with a given probability (e.g., 50%). The associated
nonconvex optimization problem can be efficiently solved by the
Difference-of-Convex functions (DC) algorithm. We prove that our estimated
policy is consistent, and its risk converges to that of the best-in-class
policy at a root-n rate. Numerical simulations show the advantage of the
proposed method over outcome modeling based benchmarks. We further demonstrate
the performance of our method in determining individualized Hemoglobin A1c
(HbA1c) control intervals for elderly patients with diabetes.
