  System stabilization via policy gradient (PG) methods has drawn increasing
attention in both control and machine learning communities. In this paper, we
study their convergence and sample complexity for stabilizing linear
time-invariant systems in terms of the number of system rollouts. Our analysis
is built upon a discounted linear quadratic regulator (LQR) method which
alternatively updates the policy and the discount factor of the LQR problem.
Firstly, we propose an explicit rule to adaptively adjust the discount factor
by exploring the stability margin of a linear control policy. Then, we
establish the sample complexity of PG methods for stabilization, which only
adds a coefficient logarithmic in the spectral radius of the state matrix to
that for solving the LQR problem with a prior stabilizing policy. Finally, we
perform simulations to validate our theoretical findings and demonstrate the
effectiveness of our method on a class of nonlinear systems.
