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Safety is the major consideration in controlling complex dynamical systemsusing reinforcement learning (RL), where the safety certificate can provideprovable safety guarantee. A valid safety certificate is an energy functionindicating that safe states are with low energy, and there exists acorresponding safe control policy that allows the energy function to alwaysdissipate. The safety certificate and the safe control policy are closelyrelated to each other and both challenging to synthesize. Therefore, existinglearning-based studies treat either of them as prior knowledge to learn theother, which limits their applicability with general unknown dynamics. Thispaper proposes a novel approach that simultaneously synthesizes theenergy-function-based safety certificate and learns the safe control policywith CRL. We do not rely on prior knowledge about either an availablemodel-based controller or a perfect safety certificate. In particular, weformulate a loss function to optimize the safety certificate parameters byminimizing the occurrence of energy increases. By adding this optimizationprocedure as an outer loop to the Lagrangian-based constrained reinforcementlearning (CRL), we jointly update the policy and safety certificate parametersand prove that they will converge to their respective local optima, the optimalsafe policy and a valid safety certificate. We evaluate our algorithms onmultiple safety-critical benchmark environments. The results show that theproposed algorithm learns provably safe policies with no constraint violation.The validity or feasibility of synthesized safety certificate is also verifiednumerically.

Joint Synthesis of Safety Certificate and Safe Control Policy using Constrained Reinforcement Learning