A socially assistive robot has the potential to augment and assist physical therapy sessions for patients with neurological and musculoskeletal problems (e.g. stroke). However, the interaction between humans and robots is still limited. For instance, prior work on a robotic exercise coach mainly utilizes pre-defined corrective feedback even if patients have various physical conditions. This research focuses on the domain of stroke rehabilitation for a robotic exercise coach and explores various techniques for more intelligent and personalized human-robot interaction for physical therapy.