Inverse Linear Quadratic Gaussian Games: Constrained Setting and Transferability

Abstract: This work addresses finite-horizon inverse linear quadratic Gaussian games. In a constrained setting, we characterize the set of cost parameters and optimal dual values that generate a given generalized Nash equilibrium, and we propose an algorithm to compute these parameters. In an unconstrained setting, we address transferability, namely, we bound the cost value perturbation between two policies: one induced by the identified cost parameters, the other by the expert parameters, under a set of different dynamics. This cost value perturbation scales linearly with the deviations in the dynamics and the identified cost parameters. Through numerical simulations, we show that, in a constrained setting, our algorithm identifies the cost parameters and dual values that can reproduce the policy and trajectories corresponding to the observed generalized Nash equilibrium. In an unconstrained setting, we show with a traffic simulation and real-robot experiments that the identified cost parameters can be used to control sufficiently close dynamics, with performance degrading linearly with the deviations in the dynamics and the identified cost parameters.