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

In modern online platforms, incentives (e.g., discounts, bonus) 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 (MCKP). The objective of this optimization is to select the optimal incentive for each customer to maximize the return on investment (ROI). 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) There is an optimality gap between the two stages, resulting 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 the budget constraint. 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 differentiable 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.