  Marketing is an important mechanism to increase user engagement and improve
platform revenue, and heterogeneous causal learning can help develop more
effective strategies. Most decision-making problems in marketing can be
formulated as resource allocation problems and have been studied for decades.
Existing works usually divide the solution procedure into two fully decoupled
stages, i.e., machine learning (ML) and operation research (OR) -- the first
stage predicts the model parameters and they are fed to the optimization in the
second stage. However, the error of the predicted parameters in ML cannot be
respected and a series of complex mathematical operations in OR lead to the
increased accumulative errors. Essentially, the improved precision on the
prediction parameters may not have a positive correlation on the final solution
due to the side-effect from the decoupled design.
  In this paper, we propose a novel approach for solving resource allocation
problems to mitigate the side-effects. Our key intuition is that we introduce
the decision factor to establish a bridge between ML and OR such that the
solution can be directly obtained in OR by only performing the sorting or
comparison operations on the decision factor. Furthermore, we design a
customized loss function that can conduct direct heterogeneous causal learning
on the decision factor, an unbiased estimation of which can be guaranteed when
the loss converges. As a case study, we apply our approach to two crucial
problems in marketing: the binary treatment assignment problem and the budget
allocation problem with multiple treatments. Both large-scale simulations and
online A/B Tests demonstrate that our approach achieves significant improvement
compared with state-of-the-art.
