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Emerging applications in robotics and autonomous systems, such as autonomousdriving and robotic surgery, often involve critical safety constraints thatmust be satisfied even when information about system models is limited. In thisregard, we propose a model-free safety specification method that learns themaximal probability of safe operation by carefully combining probabilisticreachability analysis and safe reinforcement learning (RL). Our approachconstructs a Lyapunov function with respect to a safe policy to restrain eachpolicy improvement stage. As a result, it yields a sequence of safe policiesthat determine the range of safe operation, called the safe set, whichmonotonically expands and gradually converges. We also develop an efficientsafe exploration scheme that accelerates the process of identifying the safetyof unexamined states. Exploiting the Lyapunov shielding, our method regulatesthe exploratory policy to avoid dangerous states with high confidence. Tohandle high-dimensional systems, we further extend our approach to deep RL byintroducing a Lagrangian relaxation technique to establish a tractableactor-critic algorithm. The empirical performance of our method is demonstratedthrough continuous control benchmark problems, such as a reaching task on aplanar robot arm.

Safe reinforcement learning for probabilistic reachability and safety specifications: A Lyapunov-based approach