  This paper studies an infinite horizon optimal control problem for
discrete-time linear system and quadratic criteria, both with random parameters
which are independent and identically distributed with respect to time. In this
general setting, we apply the policy gradient method, a reinforcement learning
technique, to search for the optimal control without requiring knowledge of
statistical information of the parameters. We investigate the sub-Gaussianity
of the state process and establish global linear convergence guarantee for this
approach based on assumptions that are weaker and easier to verify compared to
existing results. Numerical experiments are presented to illustrate our result.
