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Wasserstein Policy Learning for Distributional Outcomes

arXiv 2606.19117 ↗First posted 17 Jun 2026stat.ME cs.LG econ.EMcited by 0

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Abstract (arXiv)

Offline policy learning has received growing attention in causal inference. The primary objective is to learn a policy (individualized treatment rule) as a mapping from covariates to treatment that maximizes the empirical welfare defined as the mean of scalar-valued potential outcomes. In this paper, we study offline policy learning with distribution-valued outcomes, where each potential outcome is a probability measure on ℝ and the reward is defined through a utility functional applied to the Wasserstein barycenter of induced outcome distributions. We establish statistical guarantees for the policy learning framework based on both Inverse Probability Weighting (IPW) and Doubly Robust (DR) estimators. By handling the challenging uniform deviation over the product of the combinatorial policy class and the infinite-dimensional quantile domain, we prove that the finite-sample regret has leading dependence widetildeO(√mathrmN-dim(Pi)/N). In the one-dimensional Wasserstein setting and under the stated regularity conditions, the leading regret rate is still governed by the policy-class complexity. Moreover, we provide a minimax lower bound establishing the sharpness of the leading dependence on N and mathrmN-dim(Pi).

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References · 22

  1. 2018Statistical Aspects of Wasserstein Distancescited by 203
  2. 2018Confounding-Robust Policy Improvementcited by 76
  3. 2018Policy Evaluation and Optimization with Continuous Treatmentscited by 58
  4. 2017Balanced Policy Evaluation and Learningcited by 52
  5. 2015Residual Weighted Learning for Estimating Individualized Treatment Rulescited by 38
  6. 2022Doubly Robust Distributionally Robust Off-Policy Evaluation and Learningcited by 34
  7. 2022Policy learning "without" overlap: Pessimism and generalized empirical Bernstein's inequalitycited by 32
  8. 2020Learning Optimal Distributionally Robust Individualized Treatment Rulescited by 28
  9. 2019Semi-Parametric Efficient Policy Learning with Continuous Actionscited by 26
  10. 2021Policy Learning with Adaptively Collected Datacited by 21
  11. 2020Distributionally Robust Batch Contextual Banditscited by 20
  12. 2021Causal Inference on Distribution Functionscited by 11
10 more
  1. 2021Risk Minimization from Adaptively Collected Data: Guarantees for Supervised and Policy Learningcited by 10
  2. 2023Wasserstein Distributionally Robust Policy Evaluation and Learning for Contextual Banditscited by 10
  3. 2023Causal inference with a functional outcomecited by 8
  4. 2024Geodesic Causal Inferencecited by 7
  5. 2023Positivity-free Policy Learning with Observational Datacited by 6
  6. 2023Policy Learning with Distributional Welfarecited by 5
  7. 2025Doubly robust estimation of causal effects for random object outcomes with continuous treatmentscited by 5
  8. 2023Off-policy evaluation beyond overlap: partial identification through smoothnesscited by 4
  9. 2025Doubly-Robust Functional Average Treatment Effect Estimationcited by 4
  10. 2025Kernel-based estimators for functional causal effectscited by 3

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