Abstract: Covariate adjustment is often used for estimation of population average causal effects (ATE). In recent years graphical rules have been derived for determining, from a causal diagram, all covariate adjustment sets. Restricting attention to causal linear models, a very recent article introduced two graphical criterions: one to compare the asymptotic variance of linear regression estimators that control for certain distinct adjustment sets and a second to identify the optimal adjustment set that provides the smallest asymptotic variance. In this talk, I will show that the same graphical criterions can be used in arbitrary causal diagrams when the goal is to minimize the asymptotic variance of non-parametric estimators of ATE that ignore the causal diagram assumptions. Furthermore, I will provide a graphical criterion to determine the optimal adjustment set among the minimal adjustment sets. In addition, I will provide another graphical criterion for determining when a non-parametric estimator of ATE is as efficient as an efficient estimator that exploits the causal diagram assumptions. Finally, I will show that for estimating the effect of time dependent treatments in the presence of time dependent confounders, there exist diagrams with no optimal adjustment sets.