Certification of Iterative Predictions in Bayesian Neural Networks
This work addresses safety certification for control and reinforcement learning systems using BNNs, which is an incremental advancement in probabilistic verification methods.
The paper tackles the problem of computing safety guarantees for iterative predictions made by Bayesian neural networks (BNNs) by developing a method to compute lower bounds on reach-avoid probabilities, and demonstrates its application in certifying and synthesizing control policies with significant improvements in certification bounds on benchmarks.
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.