Metalearners for Ranking Treatment Effects

TL;DR

This paper tackles the problem of allocating treatments under budget constraints by learning to rank instances according to their incremental profit, rather than estimating exact treatment effects. It introduces ranking-based metalearners that extend causal meta-learners to pointwise, pairwise, and listwise objectives, with a listwise objective that directly optimizes the area under the Qini/AUQC curve. The authors demonstrate that directly optimizing the ranking can yield better decision quality than traditional effect-estimation pipelines, supported by synthetic and real-world experiments across multiple datasets. The work lays a foundation for scalable, decision-focused treatment allocation and suggests directions for further calibration, complex constraints, and extensions to observational or continuous-treatment settings.

Abstract

Efficiently allocating treatments with a budget constraint constitutes an important challenge across various domains. In marketing, for example, the use of promotions to target potential customers and boost conversions is limited by the available budget. While much research focuses on estimating causal effects, there is relatively limited work on learning to allocate treatments while considering the operational context. Existing methods for uplift modeling or causal inference primarily estimate treatment effects, without considering how this relates to a profit maximizing allocation policy that respects budget constraints. The potential downside of using these methods is that the resulting predictive model is not aligned with the operational context. Therefore, prediction errors are propagated to the optimization of the budget allocation problem, subsequently leading to a suboptimal allocation policy. We propose an alternative approach based on learning to rank. Our proposed methodology directly learns an allocation policy by prioritizing instances in terms of their incremental profit. We propose an efficient sampling procedure for the optimization of the ranking model to scale our methodology to large-scale data sets. Theoretically, we show how learning to rank can maximize the area under a policy's incremental profit curve. Empirically, we validate our methodology and show its effectiveness in practice through a series of experiments on both synthetic and real-world data.

Figures (8)

• Figure 1: Evaluating a Treatment Allocation Policy. We compare targeting policies using a Qini curve, depicting the cumulative total effect of a policy for a number of treated instances, summarized by the area under the Qini curve (AUQC).
• Figure 2: Ranking Quality for Different Objectives and Metalearners. For each metalearner, we compare a point-, pair-, and listwise version. We show the AUQC $\pm$ one standard error, scaled to have the best result $= 1$, for five different data sets.
• Figure 3: Analyzing Performance Trade-offs on Synthetic Data. We compare the three different objectives (point-, pair-, and listwise) across metalearners. Using the Synthetic data set, we compare performance in terms of MSE (i.e., pointwise accuracy), Kendall $\tau$ (i.e., pairwise rank correlation), and AUQC (i.e., listwise decision quality). For each, we show the correlation $\rho$.
• Figure 4: What Is the Effect of the Number of Sampling Iterations $k$? We show performance in terms of AUQC for the different metalearners on the Synthetic data set. We fix the sigmoid parameter $\sigma = 1$ and train with default hyperparameters.
• Figure 5: Ranking Quality for Different Objectives and Metalearners. For each metalearner, we compare three different objectives: point-, pair-, and listwise. We show performance in terms of AUQC $\pm$ one standard error, for five different data sets. As opposed to the figure in the main body, we do not scale the results here. Due to confidentiality reasons, we cannot share the raw results for the Promotion data set.

Theorems & Definitions (1)

• proof