  We explore reinforcement learning methods for finding the optimal policy in
the linear quadratic regulator (LQR) problem. In particular, we consider the
convergence of policy gradient methods in the setting of known and unknown
parameters. We are able to produce a global linear convergence guarantee for
this approach in the setting of finite time horizon and stochastic state
dynamics under weak assumptions. The convergence of a projected policy gradient
method is also established in order to handle problems with constraints. We
illustrate the performance of the algorithm with two examples. The first
example is the optimal liquidation of a holding in an asset. We show results
for the case where we assume a model for the underlying dynamics and where we
apply the method to the data directly. The empirical evidence suggests that the
policy gradient method can learn the global optimal solution for a larger class
of stochastic systems containing the LQR framework and that it is more robust
with respect to model mis-specification when compared to a model-based
approach. The second example is an LQR system in a higher dimensional setting
with synthetic data.
