Active Inverse Learning in Stackelberg Trajectory Games

Abstract: Game-theoretic inverse learning is the problem of inferring a player's 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 best describes the follower's objective function. Instead of using passively observed trajectories like existing methods, we actively maximize the differences in the follower's trajectories under different hypotheses by optimizing the leader's control inputs. Compared with uniformly random inputs, the optimized inputs accelerate the convergence of the estimated probability of different hypotheses conditioned on the follower's trajectory. We demonstrate the proposed method in a receding-horizon repeated trajectory game and simulate the results using virtual TurtleBots in Gazebo.