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

**Authors:** Zexu Sun, Hao Yang an Dugang Liu, Yunpeng Weng, Xing Tang, Xiuqiang He  
**arXiv:** [2408.11623](https://arxiv.org/abs/2408.11623)  
**Date:** 2024-08-21  
**Summary page:** https://www.summarizepaper.com/en/paper/2408.11623v1/

## Key points

- Incentives are crucial for driving user engagement and boosting platform revenue in modern online platforms.
- Uplift modeling is used to effectively allocate incentives to individual customers.
- The multi-choice knapsack problem arises when incentivizing customers within specific budget constraints, aiming to maximize return on investment.
- Traditional two-stage approaches faced challenges in optimal allocation performance due to a gap between stages and overlooking essential domain knowledge.
- The novel End-to-End Cost-Effective Incentive Recommendation (E3IR) model was proposed to address these challenges under budget constraints.
- E3IR consists of two key modules: the uplift prediction module and the differentiable allocation module, integrating integer linear programming (ILP).
- Extensive experiments showed that E3IR significantly enhanced allocation performance compared to existing two-stage approaches.
- The research by Zexu Sun, Hao Yang, Dugang Liu, Yunpeng Weng, Xing Tang, and Xiuqiang He led to an accepted paper at RecSys 2024 conference.

## Summary

In the realm of modern online platforms, incentives play a crucial role in driving user engagement and boosting platform revenue. The concept of uplift modeling has emerged as a strategic method to allocate incentives effectively to individual customers. However, many online platforms face the challenge of incentivizing customers within specific budget constraints, leading to the formulation of the multi-choice knapsack problem. This optimization problem aims to determine the optimal incentive for each customer in order to maximize return on investment. Traditionally, addressing this budget allocation issue involved a two-stage approach. Yet, this method encountered several challenges. Firstly, causal inference methods often overlooked essential domain knowledge in online marketing, where it is crucial for the expected response curve of a customer to be both monotonic and smooth as incentives increase. Secondly, an optimality gap between the two stages resulted in sub-optimal allocation performance due to the loss of incentive recommendation information for uplift prediction under limited budget constraints. To tackle these challenges head-on, a novel End-to-End Cost-Effective Incentive Recommendation (E3IR) model was proposed under budget constraints. This innovative approach consists of two key modules: the uplift prediction module and the differentiable allocation module. In the uplift prediction module, prediction heads were constructed to capture incremental improvement between adjacent treatments while adhering to marketing domain constraints such as monotonicity and smoothness. Additionally, integer linear programming (ILP) was integrated as a differentiable layer input in the allocation module. Extensive experiments conducted on both public and real product datasets showcased that E3IR significantly enhanced allocation performance compared to existing two-stage approaches. The research conducted by Zexu Sun, Hao Yang an Dugang Liu, Yunpeng Weng, Xing Tang, and Xiuqiang He culminated in an accepted paper at RecSys 2024 conference. This groundbreaking work not only addresses critical challenges in budget-constrained incentive allocation but also paves the way for more effective strategies in optimizing return on investment within online platforms through advanced modeling techniques and domain-specific knowledge integration.