Safe Online Learning Using Barrier Functions

We present a method for guaranteeing the safety of online learning schemes. The method uses barrier certificates and Sums-of-Squares programming to find a safe region of state space and a controller which renders that space positively invariant. This safe set and controller are then used to create ”training wheels”, which can be added to any controller to create a guaranteed safe controller. These training wheels alter the given controller only when the state approaches the edge of the guaranteed safe region in state space. Thus, except for where it would otherwise lead to falling, the original controller remains unchanged. For a given learning scheme, this projection is performed for each controller rollout to generate a safety guarantee for the scheme with minimal interference. We present simulation results for a simple car model and a simple hopping model, and plan to demonstrate safe learning of a walking controller for a compass gait walker.