Orthogonal Policy Learning Under Ambiguity

Abstract: 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.