Distributionally-Robust Policy Learning with Observational Data

Overview & Synopsis

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 treatment-effect, the estimator attains a fast rate of $\widetilde{O}(n^{-(1+α)/(2+α)})$ , interpolating between $\widetilde{O}(1/\sqrt{n})$ and $\widetilde{O}(1/n)$ as the margin parameter $α$ ranges over $[0,\infty)$. To our knowledge, this is the first work to incorporate a margin condition into the analysis of distributionally-robust policy learning, and the first to obtain fast rates in this setting. Empirically, on synthetic and semi-synthetic experiments calibrated to a welfare-to-work program, distributional robustness yields meaningful improvements over empirical welfare maximization when training and test distributions differ.