  Semiparametric efficient estimation of various multi-valued causal effects,
including quantile treatment effects, is important in economic, biomedical, and
other social sciences. Under the unconfoundedness condition, adjustment for
confounders requires estimating the nuisance functions relating outcome or
treatment to confounders nonparametrically. This paper considers a generalized
optimization framework for efficient estimation of general treatment effects
using artificial neural networks (ANNs) to approximate the unknown nuisance
function of growing-dimensional confounders. We establish a new approximation
error bound for the ANNs to the nuisance function belonging to a mixed
smoothness class without a known sparsity structure. We show that the ANNs can
alleviate the "curse of dimensionality" under this circumstance. We establish
the root-$n$ consistency and asymptotic normality of the proposed general
treatment effects estimators, and apply a weighted bootstrap procedure for
conducting inference. The proposed methods are illustrated via simulation
studies and a real data application.
