# Uplift modeling with continuous treatments: A predict-then-optimize approach

arXiv: https://arxiv.org/abs/2412.09232 · HTML: https://mlsanity.com/paper/2412.09232/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 70 references that are in the map.
- First posted on arXiv 12 Dec 2024.

## Builds on (most cited first, 20 of 20)

- [Inherent Trade-Offs in the Fair Determination of Risk Scores](https://mlsanity.com/paper/1609.05807/) (2016)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Algorithmic decision making and the cost of fairness](https://mlsanity.com/paper/1701.08230/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Decision-Focused Learning: Foundations, State of the Art, Benchmark and Future Opportunities](https://mlsanity.com/paper/2307.13565/) (2023)
- [Learning Counterfactual Representations for Estimating Individual Dose-Response Curves](https://mlsanity.com/paper/1902.00981/) (2019)
- [Fairness in Credit Scoring: Assessment, Implementation and Profit Implications](https://mlsanity.com/paper/2103.01907/) (2021)
- [VCNet and Functional Targeted Regularization For Learning Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2103.07861/) (2021)
- [Learning Optimal Fair Policies](https://mlsanity.com/paper/1809.02244/) (2018)
- [A unified survey of treatment effect heterogeneity modeling and uplift modeling](https://mlsanity.com/paper/2007.12769/) (2020)
- [Exploring Transformer Backbones for Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2202.01336/) (2022)
- [Sequential Deconfounding for Causal Inference with Unobserved Confounders](https://mlsanity.com/paper/2104.09323/) (2021)
- [Direct Heterogeneous Causal Learning for Resource Allocation Problems in Marketing](https://mlsanity.com/paper/2211.15728/) (2022)
- [Conformal Prediction for Causal Effects of Continuous Treatments](https://mlsanity.com/paper/2407.03094/) (2024)
- [Learning to rank for uplift modeling](https://mlsanity.com/paper/2002.05897/) (2020)
- [Response Transformation and Profit Decomposition for Revenue Uplift Modeling](https://mlsanity.com/paper/1911.08729/) (2019)
- [Observational-Interventional Priors for Dose-Response Learning](https://mlsanity.com/paper/1605.01573/) (2016)
- [On Prediction-Modelers and Decision-Makers: Why Fairness Requires More Than a Fair Prediction Model](https://mlsanity.com/paper/2310.05598/) (2023)
- [Retiring DeltaDP: New Distribution-Level Metrics for Demographic Parity](https://mlsanity.com/paper/2301.13443/) (2023)
- [Sources of Gain: Decomposing Performance in Conditional Average Dose Response Estimation](https://mlsanity.com/paper/2406.08206/) (2024)

## Built on by (most cited first, 4 of 4)

- [Hidden Representation Clustering with Multi-Task Representation Learning towards Robust Online Budget Allocation](https://mlsanity.com/paper/2506.00959/) (2025)
- [Principles and Guidelines for Randomized Controlled Trials in AI Evaluation](https://mlsanity.com/paper/2605.02050/) (2026)
- [Personalizing Marketplace Policies with Competing Objectives and Constrained Experiments: Evidence from a Job Marketplace](https://mlsanity.com/paper/2606.30932/) (2026)
- [Chance-constrained selection of sequential intervention strategies from counterfactual estimates](https://mlsanity.com/paper/2608.13209/) (2026)

## Abstract (arXiv)

The goal of uplift modeling is to recommend actions that optimize specific outcomes by determining which entities should receive treatment. One common approach involves two steps: first, an inference step that estimates conditional average treatment effects (CATEs), and second, an optimization step that ranks entities based on their CATE values and assigns treatment to the top k within a given budget. While uplift modeling typically focuses on binary treatments, many real-world applications are characterized by continuous-valued treatments, i.e., a treatment dose. This paper presents a predict-then-optimize framework to allow for continuous treatments in uplift modeling. First, in the inference step, conditional average dose responses (CADRs) are estimated from data using causal machine learning techniques. Second, in the optimization step, we frame the assignment task of continuous treatments as a dose-allocation problem and solve it using integer linear programming (ILP). This approach allows decision-makers to efficiently and effectively allocate treatment doses while balancing resource availability, with the possibility of adding extra constraints like fairness considerations or adapting the objective function to take into account instance-dependent costs and benefits to maximize utility. The experiments compare several CADR estimators and illustrate the trade-offs between policy value and fairness, as well as the impact of an adapted objective function. This showcases the framework's advantages and flexibility across diverse applications in healthcare, lending, and human resource management. All code is available on github.com/SimonDeVos/UMCT.