  We consider the problem of computing reach-avoid probabilities for iterative
predictions made with Bayesian neural network (BNN) models. Specifically, we
leverage bound propagation techniques and backward recursion to compute lower
bounds for the probability that trajectories of the BNN model reach a given set
of states while avoiding a set of unsafe states. We use the lower bounds in the
context of control and reinforcement learning to provide safety certification
for given control policies, as well as to synthesize control policies that
improve the certification bounds. On a set of benchmarks, we demonstrate that
our framework can be employed to certify policies over BNNs predictions for
problems of more than $10$ dimensions, and to effectively synthesize policies
that significantly increase the lower bound on the satisfaction probability.

Machine Learning