STATE: A Robust ATE Estimator of Heavy-Tailed Metrics for Variance Reduction in Online Controlled Experiments

Online controlled experiments play a crucial role in enabling data-driven decisions across a wide range of companies. Variance reduction is an effective technique to improve the sensitivity of experiments, achieving higher statistical power while using fewer samples and shorter experimental periods. However, typical variance reduction methods (e.g., regression-adjusted estimators) are built upon the intuitional assumption of Gaussian distributions and cannot properly characterize the real business metrics with heavy-tailed distributions. Furthermore, outliers diminish the correlation between pre-experiment covariates and outcome metrics, greatly limiting the effectiveness of variance reduction. In this paper, we develop a novel framework that integrates the Student's t-distribution with machine learning tools to fit heavy-tailed metrics and construct a robust average treatment effect estimator in online controlled experiments, which we call STATE. By adopting a variational EM method to optimize the loglikehood function, we can infer a robust solution that greatly eliminates the negative impact of outliers and achieves significant variance reduction. Moreover, we extend the STATE method from count metrics to ratio metrics by utilizing linear transformation that preserves unbiased estimation, whose variance reduction is more complex but less investigated in existing works. Finally, both simulations on synthetic data and long-term empirical results on Meituan experiment platform demonstrate the effectiveness of our method. Compared with the state-of-the-art estimators (CUPAC/MLRATE), STATE achieves over 50% variance reduction, indicating it can reach the same statistical power with only half of the observations, or half the experimental duration.

Decision Focused Causal Learning for Direct Counterfactual Marketing Optimization

Marketing optimization plays an important role to enhance user engagement in online Internet platforms. Existing studies usually formulate this problem as a budget allocation problem and solve it by utilizing two fully decoupled stages, i.e., machine learning (ML) and operation research (OR). However, the learning objective in ML does not take account of the downstream optimization task in OR, which causes that the prediction accuracy in ML may be not positively related to the decision quality. Decision Focused Learning (DFL) integrates ML and OR into an end-to-end framework, which takes the objective of the downstream task as the decision loss function and guarantees the consistency of the optimization direction between ML and OR. However, deploying DFL in marketing is non-trivial due to multiple technological challenges. Firstly, the budget allocation problem in marketing is a 0-1 integer stochastic programming problem and the budget is uncertain and fluctuates a lot in real-world settings, which is beyond the general problem background in DFL. Secondly, the counterfactual in marketing causes that the decision loss cannot be directly computed and the optimal solution can never be obtained, both of which disable the common gradient-estimation approaches in DFL. Thirdly, the OR solver is called frequently to compute the decision loss during model training in DFL, which produces huge computational cost and cannot support large-scale training data. In this paper, we propose a decision focused causal learning framework (DFCL) for direct counterfactual marketing optimization, which overcomes the above technological challenges. Both offline experiments and online A/B testing demonstrate the effectiveness of DFCL over the state-of-the-art methods. Currently, DFCL has been deployed in several marketing scenarios in Meituan, one of the largest online food delivery platform in the world.

Direct Heterogeneous Causal Learning for Resource Allocation Problems in Marketing

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.