  When learning policies for robotic systems from data, safety is a major
concern, as violation of safety constraints may cause hardware damage. SafeOpt
is an efficient Bayesian optimization (BO) algorithm that can learn policies
while guaranteeing safety with high probability. However, its search space is
limited to an initially given safe region. We extend this method by exploring
outside the initial safe area while still guaranteeing safety with high
probability. This is achieved by learning a set of initial conditions from
which we can recover safely using a learned backup controller in case of a
potential failure. We derive conditions for guaranteed convergence to the
global optimum and validate GoSafe in hardware experiments.
