  Data-driven individualized decision making has recently received increasing
research interests. Most existing methods rely on the assumption of no
unmeasured confounding, which unfortunately cannot be ensured in practice
especially in observational studies. Motivated by the recent proposed proximal
causal inference, we develop several proximal learning approaches to estimating
optimal individualized treatment regimes (ITRs) in the presence of unmeasured
confounding. In particular, we establish several identification results for
different classes of ITRs, exhibiting the trade-off between the risk of making
untestable assumptions and the value function improvement in decision making.
Based on these results, we propose several classification-based approaches to
finding a variety of restricted in-class optimal ITRs and develop their
theoretical properties. The appealing numerical performance of our proposed
methods is demonstrated via an extensive simulation study and one real data
application.
