Continuous Causal Forest: Extending Uplift Modeling to Multivariate and Continuous Treatments

In recent years, causal inference has become a hot topic in machine learning, and uplift models are widely used in intelligent marketing. Traditional uplift models only support binary treatment variables, which limits their applicability in scenarios such as ride‑hailing markets where treatment variables are often multidimensional and continuous.

To address this limitation, we propose the Continuous Causal Forest, an extension of the binary causal forest that can estimate treatment effects for continuous or multivariate treatments. The model builds on the causal forest framework (Athey & Wager) and uses a new node‑splitting statistic called Conditional Average Partial Effect (CAPE) to guide tree growth.

For binary treatments, the causal forest partitions the feature space recursively to obtain unbiased heterogeneous treatment effect estimates. For multivariate treatments, we treat one value as the control and the others as treated, defining the effect as the difference between each treated value and the control. By applying the binary causal forest to each binary comparison (multi‑binary causal forest) and aggregating the results, we obtain estimates for all treatment levels.

The Continuous Causal Forest further leverages the monotonic and locally linear nature of price‑demand curves. Within each leaf, we fit a simple linear regression of demand on price; the slope of this regression serves as the continuous treatment effect. This approach replaces the traditional CATE statistic with CAPE for splitting, while still using the binary treatment effect formula for final estimation.

Offline evaluation using the Qini score shows that the Continuous Causal Forest outperforms the multi‑binary causal forest. Online A/B experiments on pricing strategies in the ride‑hailing platform achieved more than 15% ROI improvement, and the model is now deployed in major cities.

We conclude that the Continuous Causal Forest successfully incorporates multivariate/continuous treatments into a single model, offering better data utilization and reduced deployment cost. Future work includes exploring non‑linear assumptions, handling non‑monotonic treatments, and extending the method to multi‑dimensional treatment effects.