SafePG: Safe and Globally Optimal Reinforcement Learning with Hard Constraints

RESUMO

We present an optimal and convergent model-free policy gradient (PG) reinforcement learning (RL) framework for controlling nonlinear dynamical systems under hard safety constraints. We first construct a class of stochastic wrapper policies centered around a deterministic controller, thereby enabling exploration in unknown environments while preserving the underlying deterministic control structure. We then define a class of parameterized safe-by-construction control policies by truncating these stochastic policies onto hard safety constraints. We next establish, via measure-theoretic arguments, that the potentially nonconvex RL objective under the truncated policy class, as well as its policy gradients, are well-defined. We then develop a model-free PG algorithm based on stochastic gradient ascent that directly searches over these truncated policies and leverage gradient dominance to establish convergence and optimality guarantees. Finally, we validate this framework through simulations on a safe quadrotor navigation problem.