We study a class of decision-making problems with one-sided feedback, where outcomes are only observable for specific actions. A typical example is bank loans, where the repayment status is known only if a loan is approved and remains undefined if rejected. In such scenarios, conventional approaches to causal decision evaluation and learning from observational data are not directly applicable. In this paper, we introduce a novel value function to evaluate decision rules that addresses the issue of undefined counterfactual outcomes. Without assuming no unmeasured confounders, we establish the identification of the value function using shadow variables. Furthermore, leveraging semiparametric theory, we derive the efficiency bound for the proposed value function and develop efficient methods for decision evaluation and learning. Numerical experiments and a real-world data application demonstrate the empirical performance of our proposed methods.

Individualized treatment rules/recommendations (ITRs) aim to improve patient outcomes by tailoring treatments to the characteristics of each individual. However, in high-dimensional treatment settings, existing methods face significant challenges due to data sparsity within treatment groups and highly unbalanced covariate distributions across groups. To address these challenges, we propose a novel calibration-weighted treatment fusion procedure that robustly balances covariates across treatment groups and fuses similar treatments using a penalized working model. The fusion procedure ensures the recovery of latent treatment group structures when either the calibration model or the outcome model is correctly specified. In the fused treatment space, practitioners can seamlessly apply state-of-the-art ITR learning methods with the flexibility to utilize a subset of covariates, thereby achieving robustness while addressing practical concerns such as fairness. We establish theoretical guarantees, including consistency, the oracle property of treatment fusion, and regret bounds when integrated with multi-armed ITR learning methods such as policy trees. Simulation studies show superior group recovery and policy value compared to existing approaches. We illustrate the practical utility of our method using EHR-derived data from patients with Chronic Lymphocytic Leukemia and Small Lymphocytic Lymphoma.

Today's top advertisers typically manage hundreds of campaigns simultaneously and consistently launch new ones throughout the year. A crucial challenge for marketing managers is determining the optimal allocation of limited budgets across various ad lines in each campaign to maximize cumulative returns, especially given the huge uncertainty in return outcomes. In this paper, we propose to formulate budget allocation as a multi-task combinatorial bandit problem and introduce a novel online budget allocation system. The proposed system: i) integrates a Bayesian hierarchical model to intelligently utilize the metadata of campaigns and ad lines and budget size, ensuring efficient information sharing; ii) provides the flexibility to incorporate diverse modeling techniques such as Linear Regression, Gaussian Processes, and Neural Networks, catering to diverse environmental complexities; and iii) employs the Thompson sampling technique to strike a balance between exploration and exploitation. Through extensive empirical evaluations with both synthetic data and real-world data from Amazon campaigns, our system demonstrates robustness and adaptability, effectively maximizing the overall cumulative returns. A Python implementation of the proposed procedure is available at https://anonymous.4open.science/r/MCMAB.

Typical off-policy evaluation (OPE) and off-policy learning (OPL) are not well-defined problems under "truncation by death", where the outcome of interest is not defined after some events, such as death. The standard OPE no longer yields consistent estimators, and the standard OPL results in suboptimal policies. In this paper, we formulate OPE and OPL using principal stratification under "truncation by death". We propose a survivor value function for a subpopulation whose outcomes are always defined regardless of treatment conditions. We establish a novel identification strategy under principal ignorability, and derive the semiparametric efficiency bound of an OPE estimator. Then, we propose multiply robust estimators for OPE and OPL. We show that the proposed estimators are consistent and asymptotically normal even with flexible semi/nonparametric models for nuisance functions approximation. Moreover, under mild rate conditions of nuisance functions approximation, the estimators achieve the semiparametric efficiency bound. Finally, we conduct experiments to demonstrate the empirical performance of the proposed estimators.