  Predictive human models often need to adapt their parameters online from
human data. This raises previously ignored safety-related questions for robots
relying on these models such as what the model could learn online and how
quickly could it learn it. For instance, when will the robot have a confident
estimate in a nearby human's goal? Or, what parameter initializations guarantee
that the robot can learn the human's preferences in a finite number of
observations? To answer such analysis questions, our key idea is to model the
robot's learning algorithm as a dynamical system where the state is the current
model parameter estimate and the control is the human data the robot observes.
This enables us to leverage tools from reachability analysis and optimal
control to compute the set of hypotheses the robot could learn in finite time,
as well as the worst and best-case time it takes to learn them. We demonstrate
the utility of our analysis tool in four human-robot domains, including
autonomous driving and indoor navigation.
