  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.
