Continuous Causal Forest: Extending Uplift Modeling to Multi‑dimensional Continuous Treatments in Ride‑hailing Pricing

In recent years, causal inference has become a hot topic in machine learning. Uplift models, as one of the most mature algorithms that combine causal inference with machine learning, are widely used in intelligent marketing. Most existing uplift models only handle binary treatment variables, which limits their applicability in ride‑hailing markets where treatment variables are often multi‑dimensional and continuous.

To address this limitation, we construct a Continuous Causal Forest model and successfully apply it to the pricing strategy of a ride‑hailing transaction market.

Background : An uplift model (also called a treatment‑effect model) estimates the effect of a treatment variable (W) on an outcome variable (Y). Unlike traditional supervised learning that predicts Y directly, uplift models focus on the treatment effect, which places them in the causal inference framework.

Current popular uplift frameworks (e.g., CausalML, pylift, grf) support binary treatments (e.g., coupon vs. no coupon) but lack support for multi‑dimensional or continuous treatments such as price.

Price is a continuous variable with theoretically infinite possible values. When we want to estimate the effect of each price point on supply‑demand, binary treatment models are insufficient.

Model Construction :

We start from the binary causal forest (Causal Forest) introduced by Susan Athey and Stefan Wager, which builds a random‑forest‑style estimator for heterogeneous treatment effects by recursively partitioning the feature space and maximizing the difference in treatment effects between child nodes.

To handle continuous treatments, we propose two extensions:

Multi‑binary uplift: treat each discrete treatment level as a separate binary problem (multi‑binary causal forest).

Continuous Causal Forest: replace the binary treatment‑effect statistic used for splitting with a new metric called Continuous Average Partial Effect (CAPE), which is the slope of a linear regression of Y on W within each node, leveraging the monotonic and locally linear assumptions of price‑demand curves.

The CAPE statistic is used only for node splitting; the final treatment‑effect estimates are still computed as conditional average treatment effects (CATE) for each treatment level.

Advantages :

Easy to implement; no extra development beyond existing binary uplift models.

Considers relationships among different treatment effects, allowing the model to share information across treatment levels.

Single model reduces training and deployment costs.

Disadvantages :

When many treatment levels exist, the number of binary models grows, increasing computational cost.

Each binary model uses only a fraction of the data (≈2/(k+1)), leading to inefficient data utilization.

Assumes monotonicity and linearity; may not hold for all variables.

Cannot extrapolate to unseen treatment values.

Evaluation :

Offline, we use Qini Score to compare the multi‑binary causal forest and the continuous causal forest. The continuous version shows superior Qini scores.

Online A/B testing of the continuous causal forest‑based pricing strategy yields a >15% ROI improvement and has been rolled out to most cities in the platform.

Future Work includes exploring non‑linear node statistics, handling non‑monotonic treatment variables, and extending the approach to multi‑dimensional treatment effects (e.g., interactions among multiple product‑line prices).

References: [1] Susan Athey & Stefan Wager, “Estimating Treatment Effects with Causal Forests: An Application”, Observational Studies, 2019. [2] Susan Athey, Julie Tibshirani & Stefan Wager, “Generalized Random Forests”, Annals of Statistics, 2019.