  Safe deployment of autonomous robots in diverse scenarios requires agents
that are capable of efficiently adapting to new environments while satisfying
constraints. In this work, we propose a practical and theoretically-justified
approach to maintaining safety in the presence of dynamics uncertainty. Our
approach leverages Bayesian meta-learning with last-layer adaptation. The
expressiveness of neural-network features trained offline, paired with
efficient last-layer online adaptation, enables the derivation of tight
confidence sets which contract around the true dynamics as the model adapts
online. We exploit these confidence sets to plan trajectories that guarantee
the safety of the system. Our approach handles problems with high dynamics
uncertainty, where reaching the goal safely is potentially initially
infeasible, by first \textit{exploring} to gather data and reduce uncertainty,
before autonomously \textit{exploiting} the acquired information to safely
perform the task. Under reasonable assumptions, we prove that our framework
guarantees the high-probability satisfaction of all constraints at all times
jointly, i.e. over the total task duration. This theoretical analysis also
motivates two regularizers of last-layer meta-learning models that improve
online adaptation capabilities as well as performance by reducing the size of
the confidence sets. We extensively demonstrate our approach in simulation and
on hardware.
