Active Inverse Learning in Stackelberg Trajectory Games
This work addresses game-theoretic inverse learning for dynamic systems, offering an incremental improvement over passive methods by actively controlling inputs to speed up hypothesis testing.
The authors tackled the problem of inferring a player's objectives from their actions in a Stackelberg trajectory game by proposing an active inverse learning method that optimizes leader inputs to maximize differences in follower trajectories under different hypotheses, accelerating convergence of probability estimates compared to random inputs.
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.