  The estimation of Average Treatment Effect (ATE) as a causal parameter is
carried out in two steps, where in the first step, the treatment and outcome
are modeled to incorporate the potential confounders, and in the second step,
the predictions are inserted into the ATE estimators such as the Augmented
Inverse Probability Weighting (AIPW) estimator. Due to the concerns regarding
the nonlinear or unknown relationships between confounders and the treatment
and outcome, there has been an interest in applying non-parametric methods such
as Machine Learning (ML) algorithms instead. Some literature proposes to use
two separate Neural Networks (NNs) where there's no regularization on the
network's parameters except the Stochastic Gradient Descent (SGD) in the NN's
optimization. Our simulations indicate that the AIPW estimator suffers
extensively if no regularization is utilized. We propose the normalization of
AIPW (referred to as nAIPW) which can be helpful in some scenarios. nAIPW,
provably, has the same properties as AIPW, that is, the double-robustness and
orthogonality properties. Further, if the first step algorithms converge fast
enough, under regulatory conditions, nAIPW will be asymptotically normal. We
also compare the performance of AIPW and nAIPW in terms of the bias and
variance when small to moderate L1 regularization is imposed on the NNs.
