  Motivated by the rising abundance of observational data with continuous
treatments, we investigate the problem of estimating the average dose-response
curve (ADRF). Available parametric methods are limited in their model space,
and previous attempts in leveraging neural network to enhance model
expressiveness relied on partitioning continuous treatment into blocks and
using separate heads for each block; this however produces in practice
discontinuous ADRFs. Therefore, the question of how to adapt the structure and
training of neural network to estimate ADRFs remains open. This paper makes two
important contributions. First, we propose a novel varying coefficient neural
network (VCNet) that improves model expressiveness while preserving continuity
of the estimated ADRF. Second, to improve finite sample performance, we
generalize targeted regularization to obtain a doubly robust estimator of the
whole ADRF curve.
