  Recent successes in reinforcement learning have lead to the development of
complex controllers for real-world robots. As these robots are deployed in
safety-critical applications and interact with humans, it becomes critical to
ensure safety in order to avoid causing harm. A first step in this direction is
to test the controllers in simulation. To be able to do this, we need to
capture what we mean by safety and then efficiently search the space of all
behaviors to see if they are safe. In this paper, we present an active-testing
framework based on Bayesian Optimization. We specify safety constraints using
logic and exploit structure in the problem in order to test the system for
adversarial counter examples that violate the safety specifications. These
specifications are defined as complex boolean combinations of smooth functions
on the trajectories and, unlike reward functions in reinforcement learning, are
expressive and impose hard constraints on the system. In our framework, we
exploit regularity assumptions on individual functions in form of a Gaussian
Process (GP) prior. We combine these into a coherent optimization framework
using problem structure. The resulting algorithm is able to provably verify
complex safety specifications or alternatively find counter examples.
Experimental results show that the proposed method is able to find adversarial
examples quickly.
