  In high-stakes applications of data-driven decision making like healthcare,
it is of paramount importance to learn a policy that maximizes the reward while
avoiding potentially dangerous actions when there is uncertainty. There are two
main challenges usually associated with this problem. Firstly, learning through
online exploration is not possible due to the critical nature of such
applications. Therefore, we need to resort to observational datasets with no
counterfactuals. Secondly, such datasets are usually imperfect, additionally
cursed with missing values in the attributes of features. In this paper, we
consider the problem of constructing personalized policies using logged data
when there are missing values in the attributes of features in both training
and test data. The goal is to recommend an action (treatment) when $\Xt$, a
degraded version of $\Xb$ with missing values, is observed. We consider three
strategies for dealing with missingness. In particular, we introduce the
\textit{conservative strategy} where the policy is designed to safely handle
the uncertainty due to missingness. In order to implement this strategy we need
to estimate posterior distribution $p(\Xb|\Xt)$, we use variational autoencoder
to achieve this. In particular, our method is based on partial variational
autoencoders (PVAE) which are designed to capture the underlying structure of
features with missing values.
