Structure-agnostic Optimality of Doubly Robust Learning for Treatment Effect Estimation
This work addresses a foundational open problem in causal inference, providing theoretical guarantees for practitioners in fields like policy evaluation, though it is incremental as it builds on existing frameworks and methods.
The paper tackles the problem of establishing statistical optimality for doubly robust estimators in average treatment effect estimation, proving that these widely used methods are optimal within a structure-agnostic framework that relies on black-box non-parametric oracles.
Average treatment effect estimation is the most central problem in causal inference with application to numerous disciplines. While many estimation strategies have been proposed in the literature, the statistical optimality of these methods has still remained an open area of investigation, especially in regimes where these methods do not achieve parametric rates. In this paper, we adopt the recently introduced structure-agnostic framework of statistical lower bounds, which poses no structural properties on the nuisance functions other than access to black-box estimators that achieve some statistical estimation rate. This framework is particularly appealing when one is only willing to consider estimation strategies that use non-parametric regression and classification oracles as black-box sub-processes. Within this framework, we prove the statistical optimality of the celebrated and widely used doubly robust estimators for both the Average Treatment Effect (ATE) and the Average Treatment Effect on the Treated (ATT), as well as weighted variants of the former, which arise in policy evaluation.