  Deep learning methods can be used to produce control policies, but certifying
their safety is challenging. The resulting networks are nonlinear and often
very large. In response to this challenge, we present OVERT: a sound algorithm
for safety verification of nonlinear discrete-time closed loop dynamical
systems with neural network control policies. The novelty of OVERT lies in
combining ideas from the classical formal methods literature with ideas from
the newer neural network verification literature. The central concept of OVERT
is to abstract nonlinear functions with a set of optimally tight piecewise
linear bounds. Such piecewise linear bounds are designed for seamless
integration into ReLU neural network verification tools. OVERT can be used to
prove bounded-time safety properties by either computing reachable sets or
solving feasibility queries directly. We demonstrate various examples of safety
verification for several classical benchmark examples. OVERT compares favorably
to existing methods both in computation time and in tightness of the reachable
set.
