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

Using offline observational data for policy evaluation and learning allows decision-makers to evaluate and learn a policy that connects characteristics and interventions. Most existing literature has focused on either discrete treatment spaces or assumed no difference in the distributions between the policy-learning and policy-deployed environments. These restrict applications in many real-world scenarios where distribution shifts are present with continuous treatment. To overcome these challenges, this paper focuses on developing a distributionally robust policy under a continuous treatment setting. The proposed distributionally robust estimators are established using the Inverse Probability Weighting (IPW) method extended from the discrete one for policy evaluation and learning under continuous treatments. Specifically, we introduce a kernel function into the proposed IPW estimator to mitigate the exclusion of observations that can occur in the standard IPW method to continuous treatments. We then provide finite-sample analysis that guarantees the convergence of the proposed distributionally robust policy evaluation and learning estimators. The comprehensive experiments further verify the effectiveness of our approach when distribution shifts are present.

Consumer credit services offered by electronic commerce platforms provide customers with convenient loan access during shopping and have the potential to stimulate sales. To understand the causal impact of credit lines on spending, previous studies have employed causal estimators, (e.g., direct regression (DR), inverse propensity weighting (IPW), and double machine learning (DML)) to estimate the treatment effect. However, these estimators do not treat the spending of each individual as a distribution that can capture the range and pattern of amounts spent across different orders. By disregarding the outcome as a distribution, valuable insights embedded within the outcome distribution might be overlooked. This paper thus develops distribution valued estimators which extend from existing real valued DR, IPW, and DML estimators within Rubin’s causal framework. We establish their consistency and apply them to a real dataset from a large electronic commerce platform. Our findings reveal that credit lines generally have a positive impact on spending across all quantiles, but consumers would allocate more to luxuries (higher quantiles) than necessities (lower quantiles) as credit lines increase.

The growing demand for personalized decision-making has led to a surge of interest in estimating the Conditional Average Treatment Effect (CATE). Various types of CATE estimators have been developed with advancements in machine learning and causal inference. However, selecting the desirable CATE estimator through a conventional model validation procedure remains impractical due to the absence of counterfactual outcomes in observational data. Existing approaches for CATE estimator selection, such as plug-in and pseudo-outcome metrics, face two challenges. First, they must determine the metric form and the underlying machine learning models for fitting nuisance parameters (e.g., outcome function, propensity function, and plug-in learner). Second, they lack a specific focus on selecting a robust CATE estimator. To address these challenges, this paper introduces a Distributionally Robust Metric (DRM) for CATE estimator selection. The proposed DRM is nuisance-free, eliminating the need to fit models for nuisance parameters, and it effectively prioritizes the selection of a distributionally robust CATE estimator. The experimental results validate the effectiveness of the DRM method in selecting CATE estimators that are robust to the distribution shift incurred by covariate shift and hidden confounders.

Classical domain adaptation methods acquire transferability by regularizing the overall distributional discrepancies between features in the source domain (labeled) and features in the target domain (unlabeled). They often do not differentiate whether the domain differences come from the marginals or the dependence structures. In many business and financial applications, the labeling function usually has different sensitivities to the changes in the marginals versus changes in the dependence structures. Measuring the overall distributional differences will not be discriminative enough in acquiring transferability. Without the needed structural resolution, the learned transfer is less optimal. This article proposes a new domain adaptation approach in which one can measure the differences in the internal dependence structure separately from those in the marginals. By optimizing the relative weights among them, the new regularization strategy greatly relaxes the rigidness of the existing approaches. It allows a learning machine to pay special attention to places where the differences matter the most. Experiments on three real-world datasets show that the improvements are quite notable and robust compared to various benchmark domain adaptation models.

Credit policy evaluation presents profitable opportunities for E-commerce platforms through improved decision-making. The core of policy evaluation is estimating the causal effects of the policy on the target outcome. However, selection bias presents a key challenge in estimating causal effects from real-world data. Some recent causal inference methods attempt to mitigate selection bias by leveraging covariate balancing in the representation space to obtain the domain-invariant features. However, it is noticeable that balanced representation learning can be accompanied by a failure of domain discrimination, resulting in the loss of domain-related information. This is referred to as the over-balancing issue. In this paper, we introduce a novel objective for representation balancing methods to do policy evaluation. In particular, we construct a doubly robust loss based on the predictions of treatment and outcomes, serving as a prerequisite for covariate balancing to deal with the over-balancing issue. In addition, we investigate how to improve treatment effect estimations by exploiting the unconfoundedness assumption. The extensive experimental results on benchmark datasets and a newly introduced credit dataset show a general outperformance of our method compared with existing methods.

Many practical decision-making problems in economics and healthcare seek to estimate the average treatment effect (ATE) from observational data. The Double/Debiased Machine Learning (DML) is one of the prevalent methods to estimate ATE in the observational study. However, the DML estimators can suffer an error-compounding issue and even give an extreme estimate when the propensity scores are misspecified or very close to 0 or 1. Previous studies have overcome this issue through some empirical tricks such as propensity score trimming, yet none of the existing literature solves this problem from a theoretical standpoint. In this paper, we propose a Robust Causal Learning (RCL) method to offset the deficiencies of the DML estimators. Theoretically, the RCL estimators i) are as consistent and doubly robust as the DML estimators, and ii) can get rid of the error-compounding issue. Empirically, the comprehensive experiments show that i) the RCL estimators give more stable estimations of the causal parameters than the DML estimators, and ii) the RCL estimators outperform the traditional estimators and their variants when applying different machine learning models on both simulation and benchmark datasets.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Inquisitive probing questions come naturally to humans in a variety of settings, but is a challenging task for automatic systems.One natural type of question to ask tries to fill a gap in knowledge during text comprehension, like reading a news article: we might ask about background information, deeper reasons behind things occurring, or more.Despite recent progress with data-driven approaches, generating such questions is beyond the range of models trained on existing datasets.We introduce INQUISITIVE, a dataset of ∼19K questions that are elicited while a person is reading through a document.Compared to existing datasets, INQUISITIVE questions target more towards high-level (semantic and discourse) comprehension of text.We show that readers engage in a series of pragmatic strategies to seek information.Finally, we evaluate question generation models based on GPT-2 (Radford et al., 2019) and show that our model is able to generate reasonable questions although the task is challenging, and highlight the importance of context to generate INQUIS-ITIVE questions.