  Game-theoretic inverse learning is the problem of inferring the players'
objectives from their actions. We formulate an inverse learning problem in a
Stackelberg game between a leader and a follower, where each player's action is
the trajectory of a dynamical system. We propose an active inverse learning
method for the leader to infer which hypothesis among a finite set of
candidates describes the follower's objective function. Instead of using
passively observed trajectories like existing methods, the proposed method
actively maximizes the differences in the follower's trajectories under
different hypotheses to accelerate the leader's inference. We demonstrate the
proposed method in a receding-horizon repeated trajectory game. Compared with
uniformly random inputs, the leader inputs provided by the proposed method
accelerate the convergence of the probability of different hypotheses
conditioned on the follower's trajectory by orders of magnitude.
