Training Safety Control Filters Using High-dimensional and Un-labeled Data

Synthesizing control policies that preserve the safety of autonomous systems is a challenge that remains to be solved. Towards that goal, control barrier functions (CBFs) have been developed as mathematical constructs that can be used in real-time to correct safety-violating nominal actions to ones which preserve the safety of control systems. However, synthesizing CBFs using correct-by-construction methods has not been scalable. Instead, recent research has proposed data-driven approaches for learning CBFs in the form of neural networks. Two main challenges face such approaches: (1) labeling states as unsafe or safe ones requires the knowledge of the states in the backward reachable set of the failure set--the true dynamics-dependent unsafe set, and (2) in the case of systems with high-dimensional observations, such as images and point clouds, enormous amount of data is needed to train these neural observation-based CBFs, which is expensive to obtain in robotic domains. We tackle the first challenge by using inverse constraint learning to infer a neural classifier that defines the backward reachable set from expert trajectories and use it to label sampled states. This method outperforms baselines and performs comparably to a CBF trained with ground truth labels in four environments. We tackle the second challenge by using existing vision models which are pre-trained on large and diverse datasets as frozen perception backbones on top of which latent dynamics and neural observation-based CBFs are trained. Our experimental results indicate that the resulting filters are competitive with those that have access to the ground truth state.