  We study the problem of safe learning and exploration in sequential control
problems. The goal is to safely collect data samples from operating in an
environment, in order to learn to achieve a challenging control goal (e.g., an
agile maneuver close to a boundary). A central challenge in this setting is how
to quantify uncertainty in order to choose provably-safe actions that allow us
to collect informative data and reduce uncertainty, thereby achieving both
improved controller safety and optimality. To address this challenge, we
present a deep robust regression model that is trained to directly predict the
uncertainty bounds for safe exploration. We derive generalization bounds for
learning, and connect them with safety and stability bounds in control. We
demonstrate empirically that our robust regression approach can outperform the
conventional Gaussian process (GP) based safe exploration in settings where it
is difficult to specify a good GP prior.
