  Accurate estimation of conditional average treatment effects (CATE) is at the
core of personalized decision making. While there is a plethora of models for
CATE estimation, model selection is a nontrivial task, due to the fundamental
problem of causal inference. Recent empirical work provides evidence in favor
of proxy loss metrics with double robust properties and in favor of model
ensembling. However, theoretical understanding is lacking. Direct application
of prior theoretical work leads to suboptimal oracle model selection rates due
to the non-convexity of the model selection problem. We provide regret rates
for the major existing CATE ensembling approaches and propose a new CATE model
ensembling approach based on Q-aggregation using the doubly robust loss. Our
main result shows that causal Q-aggregation achieves statistically optimal
oracle model selection regret rates of $\frac{\log(M)}{n}$ (with $M$ models and
$n$ samples), with the addition of higher-order estimation error terms related
to products of errors in the nuisance functions. Crucially, our regret rate
does not require that any of the candidate CATE models be close to the truth.
We validate our new method on many semi-synthetic datasets and also provide
extensions of our work to CATE model selection with instrumental variables and
unobserved confounding.
