  Reinforcement learning (RL) has shown great success in estimating sequential
treatment strategies which take into account patient heterogeneity. However,
health-outcome information, which is used as the reward for reinforcement
learning methods, is often not well coded but rather embedded in clinical
notes. Extracting precise outcome information is a resource intensive task, so
most of the available well-annotated cohorts are small. To address this issue,
we propose a semi-supervised learning (SSL) approach that efficiently leverages
a small sized labeled data with true outcome observed, and a large unlabeled
data with outcome surrogates. In particular, we propose a semi-supervised,
efficient approach to Q-learning and doubly robust off policy value estimation.
Generalizing SSL to sequential treatment regimes brings interesting challenges:
1) Feature distribution for Q-learning is unknown as it includes previous
outcomes. 2) The surrogate variables we leverage in the modified SSL framework
are predictive of the outcome but not informative to the optimal policy or
value function. We provide theoretical results for our Q-function and value
function estimators to understand to what degree efficiency can be gained from
SSL. Our method is at least as efficient as the supervised approach, and
moreover safe as it robust to mis-specification of the imputation models.
