Infinite Time Horizon Safety of Bayesian Neural Networks

Mathias Lechner, Đorđe Žikelić, Krishnendu Chatterjee, Thomas A Henzinger

Keywords: Bayesian neural networks, BNN, safety verification

Abstract:

Bayesian neural networks (BNNs) place distributions over the weights of a neural network to model uncertainty in the data and the network's prediction.
We consider the problem of verifying safety when running a Bayesian neural network policy in a feedback loop with infinite time horizon systems.
Compared to the existing sampling-based approaches, which are inapplicable to the infinite time horizon setting, we train a separate deterministic neural network that serves as an infinite time horizon safety certificate.
In particular, we show that the certificate network guarantees the safety of the system over a subset of the BNN weight posterior's support. Our method first computes a safe weight set and then alters the BNN's weight posterior to reject samples outside this set. Moreover, we show how to extend our approach to a safe-exploration reinforcement learning setting, in order to avoid unsafe trajectories during the training of the policy.
We evaluate our approach on a series of reinforcement learning benchmarks, including non-Lyapunovian safety specifications.

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TL;DR: Verification of Bayesian neural networks in a feedback loop with infinite time horizon systems

Code: https://github.com/mlech26l/bayesian_nn_safety

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2111.03165/code)