# End-to-End Cost-Effective Incentive Recommendation under Budget Constraint with Uplift Modeling

arXiv: https://arxiv.org/abs/2408.11623 · HTML: https://mlsanity.com/paper/2408.11623/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 41 references that are in the map.
- First posted on arXiv 21 Aug 2024.

## Builds on (most cited first, 23 of 23)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Adapting Neural Networks for the Estimation of Treatment Effects](https://mlsanity.com/paper/1906.02120/) (2019)
- [Melding the Data-Decisions Pipeline: Decision-Focused Learning for Combinatorial Optimization](https://mlsanity.com/paper/1809.05504/) (2018)
- [Interior Point Solving for LP-based prediction+optimisation](https://mlsanity.com/paper/2010.13943/) (2020)
- [Estimating Treatment Effects with Causal Forests: An Application](https://mlsanity.com/paper/1902.07409/) (2019)
- [CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints](https://mlsanity.com/paper/2105.02343/) (2021)
- [Uplift Modeling with Multiple Treatments and General Response Types](https://mlsanity.com/paper/1705.08492/) (2017)
- [A unified survey of treatment effect heterogeneity modeling and uplift modeling](https://mlsanity.com/paper/2007.12769/) (2020)
- [A Unified Framework for Marketing Budget Allocation](https://mlsanity.com/paper/1902.01128/) (2019)
- [Uplift Modeling for Multiple Treatments with Cost Optimization](https://mlsanity.com/paper/1908.05372/) (2019)
- [Explicit Feature Interaction-aware Uplift Network for Online Marketing](https://mlsanity.com/paper/2306.00315/) (2023)
- [E-Commerce Promotions Personalization via Online Multiple-Choice Knapsack with Uplift Modeling](https://mlsanity.com/paper/2108.13298/) (2021)
- [Direct Heterogeneous Causal Learning for Resource Allocation Problems in Marketing](https://mlsanity.com/paper/2211.15728/) (2022)
- [Free Lunch! Retrospective Uplift Modeling for Dynamic Promotions Recommendation within ROI Constraints](https://mlsanity.com/paper/2008.06293/) (2020)
- [Lipschitz regularized Deep Neural Networks generalize and are adversarially robust](https://mlsanity.com/paper/1808.09540/) (2018)
- [LBCF: A Large-Scale Budget-Constrained Causal Forest Algorithm](https://mlsanity.com/paper/2201.12585/) (2022)
- [Model-based Constrained MDP for Budget Allocation in Sequential Incentive Marketing](https://mlsanity.com/paper/2303.01049/) (2023)
- [Spending Money Wisely: Online Electronic Coupon Allocation based on Real-Time User Intent Detection](https://mlsanity.com/paper/2008.09982/) (2020)
- [Cost-Effective Incentive Allocation via Structured Counterfactual Inference](https://mlsanity.com/paper/1902.02495/) (2019)
- [Heterogeneous Causal Learning for Effectiveness Optimization in User Marketing](https://mlsanity.com/paper/2004.09702/) (2020)
- [Adapting Neural Networks for Uplift Models](https://mlsanity.com/paper/2011.00041/) (2020)

## Built on by (most cited first, 10 of 10)

- [Multi-channel Uplift Policy Learning](https://mlsanity.com/paper/2607.28182/) (2026)
- [ACQ: A Deployed Two-Stage Framework for Automated Creative Quota Allocation in Large-Scale Online Advertising](https://mlsanity.com/paper/2412.06167/) (2024)
- [Hidden Representation Clustering with Multi-Task Representation Learning towards Robust Online Budget Allocation](https://mlsanity.com/paper/2506.00959/) (2025)
- [Mitigating Hidden Confounding by Progressive Confounder Imputation via Large Language Models](https://mlsanity.com/paper/2507.02928/) (2025)
- [Deep Learning of Continuous and Structured Policies for Aggregated Heterogeneous Treatment Effects](https://mlsanity.com/paper/2507.05511/) (2025)
- [Budget-Constrained Causal Bandits: Bridging Uplift Modeling and Sequential Decision-Making](https://mlsanity.com/paper/2604.26169/) (2026)
- [From Prediction to Incrementality: Causal Optimization for Large-Scale Targeting and Recommendation](https://mlsanity.com/paper/2608.10182/) (2026)
- [FunnelCausalNet: Funnel-aware Joint Conversion-Revenue Uplift for Multi-tier Coupon Allocation](https://mlsanity.com/paper/2608.11675/) (2026)
- [Learning to Allocate Incentives for Incentivized Advertising via Offline Model-Based Reinforcement Learning](https://mlsanity.com/paper/2608.28065/) (2026)
- [A General Framework for Budgeted Threshold Incentives on Request](https://mlsanity.com/paper/2609.29724/) (2026)

## Abstract (arXiv)

In modern online platforms, incentives are essential factors that enhance user engagement and increase platform revenue. Over recent years, uplift modeling has been introduced as a strategic approach to assign incentives to individual customers. Especially in many real-world applications, online platforms can only incentivize customers with specific budget constraints. This problem can be reformulated as the multi-choice knapsack problem. This optimization aims to select the optimal incentive for each customer to maximize the return on investment. Recent works in this field frequently tackle the budget allocation problem using a two-stage approach. However, this solution is confronted with the following challenges: (1) The causal inference methods often ignore the domain knowledge in online marketing, where the expected response curve of a customer should be monotonic and smooth as the incentive increases. (2) An optimality gap between the two stages results in inferior sub-optimal allocation performance due to the loss of the incentive recommendation information for the uplift prediction under the limited budget constraint. To address these challenges, we propose a novel End-to-End Cost-Effective Incentive Recommendation (E3IR) model under budget constraints. Specifically, our methods consist of two modules, i.e., the uplift prediction module and the differentiable allocation module. In the uplift prediction module, we construct prediction heads to capture the incremental improvement between adjacent treatments with the marketing domain constraints (i.e., monotonic and smooth). We incorporate integer linear programming (ILP) as a differentiable layer input in the allocation module. Furthermore, we conduct extensive experiments on public and real product datasets, demonstrating that our E3IR improves allocation performance compared to existing two-stage approaches.