  Autonomous systems like aircraft and assistive robots often operate in
scenarios where guaranteeing safety is critical. Methods like Hamilton-Jacobi
reachability can provide guaranteed safe sets and controllers for such systems.
However, often these same scenarios have unknown or uncertain environments,
system dynamics, or predictions of other agents. As the system is operating, it
may learn new knowledge about these uncertainties and should therefore update
its safety analysis accordingly. However, work to learn and update safety
analysis is limited to small systems of about two dimensions due to the
computational complexity of the analysis. In this paper we synthesize several
techniques to speed up computation: decomposition, warm-starting, and adaptive
grids. Using this new framework we can update safe sets by one or more orders
of magnitude faster than prior work, making this technique practical for many
realistic systems. We demonstrate our results on simulated 2D and 10D
near-hover quadcopters operating in a windy environment.
