  In this paper, we investigate a model-free optimal control design that
minimizes an infinite horizon average expected quadratic cost of states and
control actions subject to a probabilistic risk or chance constraint using
input-output data. In particular, we consider linear time-invariant systems and
design an optimal controller within the class of linear state feedback control.
Three different policy gradient (PG) based algorithms, natural policy gradient
(NPG), Gauss-Newton policy gradient (GNPG), and deep deterministic policy
gradient (DDPG), are developed, and compared with the optimal risk-neutral
linear-quadratic regulator (LQR) and a scenario-based model predictive control
(MPC) technique via numerical simulations. The convergence properties and the
accuracy of all the algorithms are compared numerically. We also establish
analytical convergence properties of the NPG and GNPG algorithms under the
known model scenario, while the proof of convergence for the unknown model
scenario is part of our ongoing work.
