Distributionally-Robust Policy Learning with Observational Data

Debmalya Mandal

Policy learning from observational data is fundamental to applications ranging from personalized medicine to welfare-program targeting, but standard approaches optimize empirical performance and may fail when the deployment distribution differs from the training distribution. We study \emph{distributionally-robust policy learning}: given observational data, we seek a policy $π\in Π$ that maximizes the worst-case policy value over an $f$-divergence ball of radius $ρ$ around the data-generating distribution. We propose an estimator built on cross-fitted doubly-robust scores for the conditional treatment effect, paired with a DRO solver that handles \texttt{KL}, $χ^2$, and \texttt{CVaR} ambiguity sets. We establish two convergence guarantees. First, the estimated policy attains the standard $\widetilde{O}(n^{-1/2})$ rate on its DRO regret, and inherits the doubly-robust property -- the rate continues to hold whenever either the outcome model or the propensity model is consistently estimated, even at slow nonparametric rates. We then propose a sample-splitting bias-correction algorithm derived from the Lagrangian dual, and show that under a Tsybakov-style margin condition on the…