  Increasing technological sophistication and widespread use of smartphones and
wearable devices provide opportunities for innovative and highly personalized
health interventions. A Just-In-Time Adaptive Intervention (JITAI) uses
real-time data collection and communication capabilities of modern mobile
devices to deliver interventions in real-time that are adapted to the
in-the-moment needs of the user. The lack of methodological guidance in
constructing data-based JITAIs remains a hurdle in advancing JITAI research
despite the increasing popularity of JITAIs among clinical scientists. In this
article, we make a first attempt to bridge this methodological gap by
formulating the task of tailoring interventions in real-time as a contextual
bandit problem. Interpretability requirements in the domain of mobile health
lead us to formulate the problem differently from existing formulations
intended for web applications such as ad or news article placement. Under the
assumption of linear reward function, we choose the reward function (the
"critic") parameterization separately from a lower dimensional parameterization
of stochastic policies (the "actor"). We provide an online actor-critic
algorithm that guides the construction and refinement of a JITAI. Asymptotic
properties of the actor-critic algorithm are developed and backed up by
numerical experiments. Additional numerical experiments are conducted to test
the robustness of the algorithm when idealized assumptions used in the analysis
of contextual bandit algorithm are breached.
