  This paper studies the problem of estimating individualized treatment rules
when treatment effects are partially identified, as it is often the case with
observational data. By drawing connections between the treatment assignment
problem and classical decision theory, we characterize several notions of
optimal treatment policies in the presence of partial identification. Our
unified framework allows to incorporate user-defined constraints on the set of
allowable policies, such as restrictions for transparency or interpretability,
while also ensuring computational feasibility. We show how partial
identification leads to a new policy learning problem where the objective
function is directionally -- but not fully -- differentiable with respect to
the nuisance first-stage. We then propose an estimation procedure that ensures
Neyman-orthogonality with respect to the nuisance components and we provide
statistical guarantees that depend on the amount of concentration around the
points of non-differentiability in the data-generating-process. The proposed
methods are illustrated using data from the Job Partnership Training Act study.
