Existing on-policy imitation learning algorithms, such as DAgger, assume access to a fixed supervisor. However, there are many settings where the supervisor may evolve during policy learning, such as a human performing a novel task or an improving algorithmic controller. We formalize imitation learning from a "converging supervisor" and provide sublinear static and dynamic regret guarantees against the best policy in hindsight with labels from the converged supervisor, even when labels during le...