Imitation Learning of Linear Noncooperative Multiagent Games: Employing Stability and Equilibrium Constraints

In this article, imitation learning (IL) methods with stability and equilibrium constraints are proposed for fitting policies of multiagent systems (MASs) from state-control input demonstrations. The collaborative control problem of the MAS is described by a linear quadratic differential game (LQDG). First, the standard IL method for policy fitting is introduced by minimizing a loss function along with a regularization function. Considering the stability requirement of the MAS, a stability constraint is added to the standard IL method. Furthermore, we also incorporate an equilibrium constraint into the standard IL method that requires the control policies to be the equilibrium solution for some LQDG problem. The proposed IL methods with stability and equilibrium constraints require solving an optimization problem with convex cost and bilinear constraints, which can be solved by using the alternating direction method of multipliers (ADMM). Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed methods.