Proximal Causal Learning of Optimal Individualized Dose Rule

Learning optimal individualized treatment regimes from observational data is of great importance in precision medicine. However, when treatment is continuous and unmeasured confounding is present, identifying such regimes remains a significant challenge. In this paper, we leverage the proximal learning framework to nonparametrically identify and estimate the optimal individualized dose rule in the presence of unmeasured confounders. Corresponding theoretical guarantees for the proposed estimators are also established, including the excess risk bound and optimal convergence rate. Simulation studies and a synthetic experiment confirm the practical utility of our framework.