Abstract
This paper studies the problem of estimating individualized treatment rules when treatment effects are partially identifed, 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 identifcation. The proposed framework allows to incorporate user-defined constraints on the policies, such as restrictions for transparency or interpretability, while also ensuring computational feasibility. We show that partial identification leads to a novel statistical learning problem with risk directionally -- but not fully -- differentiable with respect to an infinite-dimensional nuisance component. We propose an estimation procedure that ensures Neyman-orthogonality with respect to the nuisance component and provide statistical guarantees that depend on the amount of concentration around the points of non-differentiability in the data-generating process. The proposed method is illustrated using data from the Job Partnership Training Act study.