  Although learning-based methods have great potential for robotics, one
concern is that a robot that updates its parameters might cause large amounts
of damage before it learns the optimal policy. We formalize the idea of safe
learning in a probabilistic sense by defining an optimization problem: we
desire to maximize the expected return while keeping the expected damage below
a given safety limit. We study this optimization for the case of a robot
manipulator with safety-based torque limits. We would like to ensure that the
damage constraint is maintained at every step of the optimization and not just
at convergence. To achieve this aim, we introduce a novel method which predicts
how modifying the torque limit, as well as how updating the policy parameters,
might affect the robot's safety. We show through a number of experiments that
our approach allows the robot to improve its performance while ensuring that
the expected damage constraint is not violated during the learning process.
