  With the outstanding performance of policy gradient (PG) method in the
reinforcement learning field, the convergence theory of it has aroused more and
more interest recently. Meanwhile, the significant importance and abundant
theoretical researches make the stochastic linear quadratic (SLQ) control
problem a starting point for studying PG in model-based learning setting. In
this paper, we study the PG method for the SLQ problem in infinite horizon and
take a step towards providing rigorous guarantees for gradient methods.
Although the cost functional of linear-quadratic problem is typically
nonconvex, we still overcome the difficulty based on gradient domination
condition and L-smoothness property, and prove exponential/linear convergence
of gradient flow/descent algorithm.
