  Recently, many estimators for network treatment effects have been proposed.
But, their optimality properties in terms of semiparametric efficiency have yet
to be resolved. We present a simple, yet flexible asymptotic framework to
derive the efficient influence function and the semiparametric efficiency lower
bound for a family of network causal effects under partial interference. An
important corollary of our results is that one of the existing estimators by
Liu et al. (2019) is locally efficient. We also present other estimators that
are efficient and discuss results on adaptive estimation. We conclude by using
the efficient estimators to study the direct and spillover effects of
conditional cash transfer programs in Colombia.
