  We introduce two algorithms for computing tight guarantees on the
probabilistic robustness of Bayesian Neural Networks (BNNs). Computing
robustness guarantees for BNNs is a significantly more challenging task than
verifying the robustness of standard Neural Networks (NNs) because it requires
searching the parameters' space for safe weights. Moreover, tight and complete
approaches for the verification of standard NNs, such as those based on
Mixed-Integer Linear Programming (MILP), cannot be directly used for the
verification of BNNs because of the polynomial terms resulting from the
consecutive multiplication of variables encoding the weights. Our algorithms
efficiently and effectively search the parameters' space for safe weights by
using iterative expansion and the network's gradient and can be used with any
verification algorithm of choice for BNNs. In addition to proving that our
algorithms compute tighter bounds than the SoA, we also evaluate our algorithms
against the SoA on standard benchmarks, such as MNIST and CIFAR10, showing that
our algorithms compute bounds up to 40% tighter than the SoA.
