  Safety is the major consideration in controlling complex dynamical systems
using reinforcement learning (RL), where the safety certificate can provide
provable safety guarantee. A valid safety certificate is an energy function
indicating that safe states are with low energy, and there exists a
corresponding safe control policy that allows the energy function to always
dissipate. The safety certificate and the safe control policy are closely
related to each other and both challenging to synthesize. Therefore, existing
learning-based studies treat either of them as prior knowledge to learn the
other, which limits their applicability with general unknown dynamics. This
paper proposes a novel approach that simultaneously synthesizes the
energy-function-based safety certificate and learns the safe control policy
with CRL. We do not rely on prior knowledge about either an available
model-based controller or a perfect safety certificate. In particular, we
formulate a loss function to optimize the safety certificate parameters by
minimizing the occurrence of energy increases. By adding this optimization
procedure as an outer loop to the Lagrangian-based constrained reinforcement
learning (CRL), we jointly update the policy and safety certificate parameters
and prove that they will converge to their respective local optima, the optimal
safe policy and a valid safety certificate. We evaluate our algorithms on
multiple safety-critical benchmark environments. The results show that the
proposed algorithm learns provably safe policies with no constraint violation.
The validity or feasibility of synthesized safety certificate is also verified
numerically.
