Deep Spectral Q-learning with Application to Mobile Health

Precision medicine focuses on providing personalized treatment to patients by taking their personal information into consideration (see e.g., Kosorok and Laber, 2019; Tsiatis et al., 2019). It has found various applications in numerous studies, ranging from the cardiovascular disease study to cancer treatment and gene therapy (Jameson and Longo, 2015). A dynamic treatment regime (DTR) consists of a sequence of treatment decisions rules tailored to each individual patient's status at each time, mathematically formulating the idea behind precision medicine. One of the major objectives in precision medicine is to identify the optimal dynamic treatment regime that yields the most favorable outcome on average. With the rapidly development of mobile health (mHealth) technology, it becomes feasible to collect rich longitudinal data through mobile apps in medical studies.