Metamorphic relations via relaxations: an approach to obtain oracles for action-policy testing

Testing is a promising way to gain trust in a learned action policy 𝜋, in particular if 𝜋 is a neural network. A "bug" in this context constitutes undesirable or fatal policy behavior, e.g., satisfying a failure condition. But how do we distinguish whether such behavior is due to bad policy decisions, or whether it is actually unavoidable under the given circumstances? This requires knowledge about optimal solutions, which defeats the scalability of testing. Related problems occur in software testing when the correct program output is not known. Metamorphic testing addresses this issue through metamorphic relations, specifying how a given change to the input should affect the output, thus providing an oracle for the correct output. Yet, how do we obtain such metamorphic relations for action policies? Here, we show that the well explored concept of relaxations in the Artificial Intelligence community can serve this purpose. In particular, if state 𝑠 ′ is a relaxation of state 𝑠, i.e., 𝑠 ′ is easier to solve than 𝑠, and 𝜋 fails on easier 𝑠 ′ but does not fail on harder 𝑠, then we know that 𝜋 contains a bug manifested on 𝑠 ′ . We contribute the first exploration of this idea in the context of failure testing of neural network policies 𝜋 learned by reinforcement learning in simulated environments. We design fuzzing strategies for test-case generation as well as metamorphic oracles leveraging simple, manually designed relaxations. In experiments on three single-agent games, our technology is able to effectively identify true bugs, i.e., avoidable failures of 𝜋, which has not been possible until now.