Towards Safe Reinforcement Learning Using NMPC and Policy Gradients: Part I - Stochastic case

We present a methodology to deploy the stochastic policy gradient method, using actor-critic techniques, when the optimal policy is approximated using a parametric optimization problem, allowing one to enforce safety via hard constraints. For continuous input spaces, imposing safety restrictions on the stochastic policy can make the sampling and evaluation of its density difficult. This paper proposes a computationally effective approach to solve that issue. We will focus on policy approximations based on robust Nonlinear Model Predictive Control (NMPC), where safety can be treated explicitly. For the sake of brevity, we will detail safe policies 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 deterministic policy gradient case.