A Learner-Verifier Framework for Neural Network Controllers and Certificates of Stochastic Systems

Abstract Reinforcement learning has received much attention for controllers of deterministic systems. We consider a learner-verifier framework stochastic control systems and survey recent methods that formally guarantee conjunction reachability safety properties. Given property lower bound on the probability being satisfied, our jointly learns policy formal certificate to ensure satisfaction with desired threshold. Both are continuous functions from states reals, which learned as parameterized neural networks. While in case, certificates invariant barrier safety, or Lyapunov ranking liveness, case supermartingales. For verification, we use interval arithmetic abstract interpretation expected values network functions.