The Final-Stage Bottleneck: A Systematic Dissection of the R-Learner for Network Causal Inference

TL;DR

This paper systematically analyzes the R-Learner for network causal inference, revealing a critical representation bottleneck and proposing an end-to-end Graph R-Learner that outperforms traditional methods.

Contribution

It provides the first rigorous evidence of a representation bottleneck in R-Learners on graphs and introduces a successful end-to-end Graph R-Learner approach.

Findings

Graph-blind final-stage R-Learners fail completely on graph data.

End-to-end Graph R-Learner significantly outperforms non-DML GNN T-Learner.

Identifies a topology-dependent nuisance bottleneck linked to GNN over-squashing.

Abstract

The R-Learner is a powerful, theoretically-grounded framework for estimating heterogeneous treatment effects, prized for its robustness to nuisance model errors. However, its application to network data, where causal heterogeneity is often graph-dependent, presents a critical challenge to its core assumption of a well-specified final-stage model. In this paper, we conduct a large-scale empirical study to systematically dissect the R-Learner framework on graphs. We provide the first rigorous evidence that the primary driver of performance is the inductive bias of the final-stage CATE estimator, an effect that dominates the choice of nuisance models. Our central finding is the quantification of a catastrophic "representation bottleneck": we prove with overwhelming statistical significance (p < 0.001) that R-Learners with a graph-blind final stage fail completely (MSE > 4.0), even when paired with powerful GNN nuisance models. Conversely, our proposed end-to-end Graph R-Learner succeeds and significantly outperforms a strong, non-DML GNN T-Learner baseline. Furthermore, we identify and provide a mechanistic explanation for a subtle, topology-dependent "nuisance bottleneck," linking it to GNN over-squashing via a targeted "Hub-Periphery Trade-off" analysis. Our findings are validated across diverse synthetic and semi-synthetic benchmarks. We release our code as a reproducible benchmark to facilitate future research on this critical "final-stage bottleneck."