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

Zexu Sun, Hao Yang, Dugang Liu, Yunpeng Weng, Xing Tang, Xiuqiang He

TL;DR

This work tackles end-to-end budget-constrained incentive allocation by reframing uplift modeling as a cost-aware optimization problem. It introduces E3IR, a two-module architecture with a monotonic and smooth uplift prediction component and a differentiable ILP-based allocation layer that backpropagates through the optimization process. By aligning uplift prediction with the budget-constrained decision task in a joint training objective, E3IR reduces the suboptimality gap inherent in two-stage pipelines and improves ROI-focused incentive recommendations for both binary and multi-treatment settings. Extensive experiments on public and production datasets demonstrate superior performance across uplift and budget-allocation metrics, validating the practical impact for cost-effective online marketing campaigns.

Abstract

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.

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

TL;DR

This work tackles end-to-end budget-constrained incentive allocation by reframing uplift modeling as a cost-aware optimization problem. It introduces E3IR, a two-module architecture with a monotonic and smooth uplift prediction component and a differentiable ILP-based allocation layer that backpropagates through the optimization process. By aligning uplift prediction with the budget-constrained decision task in a joint training objective, E3IR reduces the suboptimality gap inherent in two-stage pipelines and improves ROI-focused incentive recommendations for both binary and multi-treatment settings. Extensive experiments on public and production datasets demonstrate superior performance across uplift and budget-allocation metrics, validating the practical impact for cost-effective online marketing campaigns.

Abstract

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.
Paper Structure (29 sections, 2 theorems, 19 equations, 6 figures, 2 tables)

This paper contains 29 sections, 2 theorems, 19 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Budget Allocation
  4. End-to-End Optimization
  5. Preliminaries
  6. Cost-aware Uplift Modeling
  7. Budget Allocation Problem
  8. Binary Treatment Budget Allocation
  9. Multi-Treatment Budget Allocation
  10. Methodology
  11. Uplift Prediction Module
  12. Monotonic Constraint
  13. Smooth Constraint
  14. Differentiable Allocation Module
  15. Descent direction
  16. ...and 14 more sections

Key Result

Proposition 1

Let $y:\mathbb{R}^{\ell} \rightarrow \mathbb{R}^n$ be a differentiable function at $x \in \mathbb{R}^{\ell}$. Let $L:\mathbb{R}^n \rightarrow \mathbb{R}$ be a differentiable function at $y = y(x) \in \mathbb{R}^n$. Denote $dy = \frac{\partial L}{\partial y}$ at $y$. Then the distance between $y(x)$

Figures (6)

  • Figure 1: An example of the common bad cases of the user response curve. $f(t)$ and $g(t)$ are a user's response function and cost function, respectively. $t^*$ is the expected best incentive level, which satisfies the $f(t^*)-\lambda g(t^*)>f(t_i)-\lambda g(t_i), \forall t_i\neq t^*$. In the two cases, we may find the wrong best incentive level $t_j$ (i.e., $t_{k+1}$ in (a) and $t_{k+4}$ in (b)) because of $f(t^*)-\lambda g(t^*)<f(t_j)-\lambda g(t_j), \forall t_j\neq t^*$.
  • Figure 2: The overall structure of our E$^3$IR. The uplift prediction module generates the predicted uplift of user responses and corresponding costs, the differentiable allocation module generates the allocation matrix, and the two loss functions $\mathcal{L}_{\text{uplift}}$ and $\mathcal{L}_{\text{allocation}}$ are jointly optimized in Eq. \ref{['eq:finalloss']}.
  • Figure 3: The visualization of the Production dataset collection subject to different treatments. As $t$ increases, the clarity of the video correspondingly enhances.
  • Figure 4: Ablation study of our E$^3$IR on all the binary treatment and multi-treatment datasets.
  • Figure 5: Cost curve comparison between the cost-aware baselines and our E$^3$IR on the multi-treatment datasets.
  • ...and 1 more figures

Theorems & Definitions (2)

  • Proposition 1
  • Proposition 2