  We consider the problem of batch multi-task reinforcement learning with
observed context descriptors, motivated by its application to personalized
medical treatment. In particular, we study two general classes of learning
algorithms: direct policy learning (DPL), an imitation-learning based approach
which learns from expert trajectories, and model-based learning. First, we
derive sample complexity bounds for DPL, and then show that model-based
learning from expert actions can, even with a finite model class, be
impossible. After relaxing the conditions under which the model-based approach
is expected to learn by allowing for greater coverage of state-action space, we
provide sample complexity bounds for model-based learning with finite model
classes, showing that there exist model classes with sample complexity
exponential in their statistical complexity. We then derive a sample complexity
upper bound for model-based learning based on a measure of concentration of the
data distribution. Our results give formal justification for imitation learning
over model-based learning in this setting.
