  We present Revel, a partially neural reinforcement learning (RL) framework
for provably safe exploration in continuous state and action spaces. A key
challenge for provably safe deep RL is that repeatedly verifying neural
networks within a learning loop is computationally infeasible. We address this
challenge using two policy classes: a general, neurosymbolic class with
approximate gradients and a more restricted class of symbolic policies that
allows efficient verification. Our learning algorithm is a mirror descent over
policies: in each iteration, it safely lifts a symbolic policy into the
neurosymbolic space, performs safe gradient updates to the resulting policy,
and projects the updated policy into the safe symbolic subset, all without
requiring explicit verification of neural networks. Our empirical results show
that Revel enforces safe exploration in many scenarios in which Constrained
Policy Optimization does not, and that it can discover policies that outperform
those learned through prior approaches to verified exploration.
