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This research advances distributionally-robust policy learning by introducing a bias-correction algorithm that achieves faster convergence rates under specific margin conditions. The proposed estimator combines cross-fitted doubly-robust scores with solvers for various ambiguity sets, offering improved reliability when deployment distributions shift from training data. Empirical results on welfare-to-work scenarios demonstrate meaningful gains in robustness over standard empirical performance optimization.
Distributionally-Robust Policy Learning with Observational Data
arXiv:2610.25591v1 Announce Type: new Abstract: 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 $\pi \in \Pi$ that maximizes the worst-case policy value over an $f$-divergence ball of radius $\rho$ 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}, $\chi^2$, 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 $\widetilde{O}(n^{-(1+\alpha)/(2+\alpha)})$ , interpolating between $\widetilde{O}(1/\sqrt{n})$ and $\widetilde{O}(1/n)$ as the margin parameter $\alpha$ 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.
Abstract: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 $\pi \in \Pi$ that maximizes the worst-case policy value over an $f$-divergence ball of radius $\rho$ 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}, $\chi^2$, 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 $\widetilde{O}(n^{-(1+\alpha)/(2+\alpha)})$ , interpolating between $\widetilde{O}(1/\sqrt{n})$ and $\widetilde{O}(1/n)$ as the margin parameter $\alpha$ 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.
To appear at NeurIPS 2026. Generative AI was used only to polish writing and implement the main algorithm
Machine Learning (cs.LG)
arXiv:2610.25591 [cs.LG]
(or arXiv:2610.25591v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.25591 Focus to learn more arXiv-issued DOI via DataCite
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