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 $\mathbb{R}$ 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 $\widetilde{\mathcal{O}}(\sqrt{\mathrm{N\text{-}dim}(Π)/N})$. 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 $\mathrm{N\text{-}dim}(Π)$.

Estimating individualized treatment rules (ITRs) is fundamental in causal inference, particularly for precision medicine applications. Traditional ITR estimation methods rely on inverse probability weighting (IPW) to address confounding factors and $L_{1}$-penalization for simplicity and interpretability. However, IPW can introduce statistical bias without precise propensity score modeling, while $L_1$-penalization makes the objective non-smooth, leading to computational bias and requiring subgradient methods. In this paper, we propose a unified ITR estimation framework formulated as a constrained, weighted, and smooth convex optimization problem. The optimal ITR can be robustly and effectively computed by projected gradient descent. Our comprehensive theoretical analysis reveals that weights that balance the spectrum of a `weighted design matrix' improve both the optimization and likelihood landscapes, yielding improved computational and statistical estimation guarantees. In particular, this is achieved by distributional covariate balancing weights, which are model-free alternatives to IPW. Extensive simulations and applications demonstrate that our framework achieves significant gains in both robustness and effectiveness for ITR learning against existing methods.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Double robustness is a major selling point of semiparametric and missing data methodology. Its virtues lie in protection against partial nuisance misspecification and asymptotic semiparametric efficiency under correct nuisance specification. However, in many applications, complete nuisance misspecification should be regarded as the norm (or at the very least the expected default), and thus doubly robust estimators may behave fragilely. In fact, it has been amply verified empirically that these estimators can perform poorly when all nuisance functions are misspecified. Here, we first characterize this phenomenon of double fragility, and then propose a solution based on adaptive correction clipping (ACC). We argue that our ACC proposal is safe, in that it inherits the favorable properties of doubly robust estimators under correct nuisance specification, but its error is guaranteed to be bounded by a convex combination of the individual nuisance model errors, which prevents the instability caused by the compounding product of errors of doubly robust estimators. We also show that our proposal provides valid inference through the parametric bootstrap when nuisances are well-specified. We showcase the efficacy of our ACC estimator both through extensive simulations and by applying it to the analysis of Alzheimer's disease proteomics data.

Recursive decision trees have emerged as a leading methodology for heterogeneous causal treatment effect estimation and inference in experimental and observational settings. These procedures are fitted using the celebrated CART (Classification And Regression Tree) algorithm [Breiman et al., 1984], or custom variants thereof, and hence are believed to be "adaptive" to high-dimensional data, sparsity, or other specific features of the underlying data generating process. Athey and Imbens [2016] proposed several "honest" causal decision tree estimators, which have become the standard in both academia and industry. We study their estimators, and variants thereof, and establish lower bounds on their estimation error. We demonstrate that these popular heterogeneous treatment effect estimators cannot achieve a polynomial-in-$n$ convergence rate under basic conditions, where $n$ denotes the sample size. Contrary to common belief, honesty does not resolve these limitations and at best delivers negligible logarithmic improvements in sample size or dimension. As a result, these commonly used estimators can exhibit poor performance in practice, and even be inconsistent in some settings. Our theoretical insights are empirically validated through simulations.

Estimating causal effects from observational data is challenging due to selection bias, which leads to imbalanced covariate distributions across treatment groups. Propensity score-based weighting methods are widely used to address this issue by reweighting samples to simulate a randomized controlled trial (RCT). However, the effectiveness of these methods heavily depends on the observed data and the accuracy of the propensity score estimator. For example, inverse propensity weighting (IPW) assigns weights based on the inverse of the propensity score, which can lead to instable weights when propensity scores have high variance-either due to data or model misspecification-ultimately degrading the ability of handling selection bias and treatment effect estimation. To overcome these limitations, we propose Deconfounding Factor Weighting (DFW), a novel propensity score-based approach that leverages the deconfounding factor-to construct stable and effective sample weights. DFW prioritizes less confounded samples while mitigating the influence of highly confounded ones, producing a pseudopopulation that better approximates a RCT. Our approach ensures bounded weights, lower variance, and improved covariate balance.While DFW is formulated for binary treatments, it naturally extends to multi-treatment settings, as the deconfounding factor is computed based on the estimated probability of the treatment actually received by each sample. Through extensive experiments on real-world benchmark and synthetic datasets, we demonstrate that DFW outperforms existing methods, including IPW and CBPS, in both covariate balancing and treatment effect estimation.

Off-Policy Evaluation (OPE) aims to estimate the value of a target policy using offline data collected from potentially different policies. In real-world applications, however, logged data often suffers from missingness. While OPE has been extensively studied in the literature, a theoretical understanding of how missing data affects OPE results remains unclear. In this paper, we investigate OPE in the presence of monotone missingness and theoretically demonstrate that the value estimates remain unbiased under ignorable missingness but can be biased under nonignorable (informative) missingness. To retain the consistency of value estimation, we propose an inverse probability weighted value estimator and conduct statistical inference to quantify the uncertainty of the estimates. Through a series of numerical experiments, we empirically demonstrate that our proposed estimator yields a more reliable value inference under missing data.

Estimating individualized treatment rules (ITRs) is fundamental in causal inference, particularly for precision medicine applications. Traditional ITR estimation methods rely on inverse probability weighting (IPW) to address confounding factors and L_{1} -penalization for simplicity and interpretability. However, IPW can introduce statistical bias without precise propensity score modeling, while L_1 -penalization makes the objective non-smooth, leading to computational bias and requiring subgradient methods. In this paper, we propose a unified ITR estimation framework formulated as a constrained, weighted, and smooth convex optimization problem. The optimal ITR can be robustly and effectively computed by projected gradient descent.

A key quantity in the analysis is p_j, the probability of missing j-th feature. Is this quantity given in advanced? Under MCAR, it can be easily estimated. But some clarifications are needed. Essentially, this method is just SGD IPW (though it is coordinate-wise IPW not the regular IPW).