Before revision:  Under reasonable assumptions, we prove that our framework provides safety guarantees in the form of a single joint chance constraint. Furthermore, we use this theoretical analysis to motivate regularization of the model to improve performance .
After revision:  Under reasonable assumptions, we prove that our framework has high-probability guarantees of satisfying all constraints at all times jointly. This analysis also motivates two regularizers of last-layer meta-learners that improve online adaptation capabilities as well as performance by reducing the size of the confidence sets .