  In this paper, we present a methodology to deploy the deterministic policy
gradient method, using actor-critic techniques, when the optimal policy is
approximated using a parametric optimization problem, where safety is enforced
via hard constraints. For continuous input space, imposing safety restrictions
on the exploration needed to deploying the deterministic policy gradient method
poses some technical difficulties, which we address here. We will investigate
in particular policy approximations based on robust Nonlinear Model Predictive
Control (NMPC), where safety can be treated explicitly. For the sake of
brevity, we will detail the construction of the safe scheme in the robust
linear MPC context only. The extension to the nonlinear case is possible but
more complex. We will additionally present a technique to maintain the system
safety throughout the learning process in the context of robust linear MPC.
This paper has a companion paper treating the stochastic policy gradient case.
