  This article studies inverse reinforcement learning (IRL) for the stochastic
linear-quadratic optimal control problem, where two agents are considered. A
learner agent does not know the expert agent's performance cost function, but
it imitates the behavior of the expert agent by constructing an underlying cost
function that obtains the same optimal feedback control as the expert's. We
first develop a model-based IRL algorithm, which consists of a policy
correction and a policy update from the policy iteration in reinforcement
learning, as well as a cost function weight reconstruction based on the inverse
optimal control. Then, under this scheme, we propose a model-free off-policy
IRL algorithm, which does not need to know or identify the system and only
needs to collect the behavior data of the expert agent and learner agent once
during the iteration process. Moreover, the proofs of the algorithm's
convergence, stability, and non-unique solutions are given. Finally, a
simulation example is provided to verify the effectiveness of the proposed
algorithm.
