Vanilla Reinforcement Learning (RL) can efficiently solve complex tasks but does not provide any guarantees on system behavior. To bridge this gap, we propose a three-step safe RL procedure for continuous action spaces that provides probabilistic guarantees with respect to temporal logic specifications. First, our approach probabilistically verifies a candidate controller with respect to a temporal logic specification while randomizing the control inputs to the system within a bounded set. Second, we improve the performance of this probabilistically verified controller by adding an RL agent that optimizes the verified controller for performance in the same bounded set around the control input. Third, we verify probabilistic safety guarantees with respect to temporal logic specifications for the learned agent. Our approach is efficiently implementable for continuous action and state spaces. The separation of safety verification and performance improvement into two distinct steps realizes both explicit probabilistic safety guarantees and a straightforward RL setup that focuses on performance. We evaluate our approach on an evasion task where a robot has to reach a goal while evading a dynamic obstacle with a specific maneuver. Our results show that our safe RL approach leads to efficient learning while maintaining its probabilistic safety specification.

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