  Online platforms often incentivize consumers to improve user engagement and
platform revenue. Since different consumers might respond differently to
incentives, individual-level budget allocation is an essential task in
marketing campaigns. Recent advances in this field often address the budget
allocation problem using a two-stage paradigm: the first stage estimates the
individual-level treatment effects using causal inference algorithms, and the
second stage invokes integer programming techniques to find the optimal budget
allocation solution. Since the objectives of these two stages might not be
perfectly aligned, such a two-stage paradigm could hurt the overall marketing
effectiveness.
  In this paper, we propose a novel end-to-end framework to directly optimize
the business goal under budget constraints. Our core idea is to construct a
regularizer to represent the marketing goal and optimize it efficiently using
gradient estimation techniques. As such, the obtained models can learn to
maximize the marketing goal directly and precisely. We extensively evaluate our
proposed method in both offline and online experiments, and experimental
results demonstrate that our method outperforms current state-of-the-art
methods. Our proposed method is currently deployed to allocate marketing
budgets for hundreds of millions of users on a short video platform and
achieves significant business goal improvements. Our code will be publicly
available.
