Title: Markov Decision Processes with Continuous Side Information,
Abstract: We consider a reinforcement learning (RL) setting in which the agent
interacts with a sequence of episodic MDPs. At the start of each episode the
agent has access to some side-information or context that determines the
dynamics of the MDP for that episode. Our setting is motivated by applications
in healthcare where baseline measurements of a patient at the start of a
treatment episode form the context that may provide information about how the
patient might respond to treatment decisions. We propose algorithms for
learning in such Contextual Markov Decision Processes (CMDPs) under an
assumption that the unobserved MDP parameters vary smoothly with the observed
context. We also give lower and upper PAC bounds under the smoothness
assumption. Because our lower bound has an exponential dependence on the
dimension, we consider a tractable linear setting where the context is used to
create linear combinations of a finite set of MDPs. For the linear setting, we
give a PAC learning algorithm based on KWIK learning techniques.