  We study the global convergence of generative adversarial imitation learning
for linear quadratic regulators, which is posed as minimax optimization. To
address the challenges arising from non-convex-concave geometry, we analyze the
alternating gradient algorithm and establish its Q-linear rate of convergence
to a unique saddle point, which simultaneously recovers the globally optimal
policy and reward function. We hope our results may serve as a small step
towards understanding and taming the instability in imitation learning as well
as in more general non-convex-concave alternating minimax optimization that
arises from reinforcement learning and generative adversarial learning.
