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Energy-function-based safety certificates can provide provable safetyguarantees for the safe control tasks of complex robotic systems. However, allrecent studies about learning-based energy function synthesis only consider thefeasibility, which might cause over-conservativeness and result in lessefficient controllers. In this work, we proposed the magnitude regularizationtechnique to improve the efficiency of safe controllers by reducing theconservativeness inside the energy function while keeping the promisingprovable safety guarantees. Specifically, we quantify the conservativeness bythe magnitude of the energy function, and we reduce the conservativeness byadding a magnitude regularization term to the synthesis loss. We propose theSafeMR algorithm that uses reinforcement learning (RL) for the synthesis tounify the learning processes of safe controllers and energy functions.Experimental results show that the proposed method does reduce theconservativeness of the energy functions and outperforms the baselines in termsof the controller efficiency while guaranteeing safety.

Synthesize Efficient Safety Certificates for Learning-Based Safe Control using Magnitude Regularization