During human-robot interaction (HRI), we want the robot to understand us, and we want to intuitively understand the robot. In order to communicate with and understand the robot, we can leverage interactions, where the human and robot observe each other's behavior. However, it is not always clear how the human and robot should interpret these actions: a given interaction might mean several different things. Within today's state-of-the-art, the robot assigns a single interaction strategy to the human, and learns from or teaches the human according to this fixed strategy. Instead, we here recognize that different users interact in different ways, and so one size does not fit all. Therefore, we argue that the robot should maintain a distribution over the possible human interaction strategies, and then infer how each individual end-user interacts during the task. We formally define learning and teaching when the robot is uncertain about the human's interaction strategy, and derive solutions to both problems using Bayesian inference. In examples and a benchmark simulation, we show that our personalized approach outperforms standard methods that maintain a fixed interaction strategy.