Risk-Averse Certification of Bayesian Neural Networks

TL;DR

This paper introduces RAC-BNN, a framework for certifying Bayesian neural networks' robustness using risk measures and polytopic output sets, providing probabilistic guarantees and improved bounds.

Contribution

It presents a novel risk-averse certification method for BNNs that incorporates CVaR and set-based output approximation, enhancing robustness evaluation.

Findings

RAC-BNN provides tighter certified bounds.

It achieves higher efficiency in complex tasks.

The method effectively quantifies robustness under risky scenarios.

Abstract

In light of the inherently complex and dynamic nature of real-world environments, incorporating risk measures is crucial for the robustness evaluation of deep learning models. In this work, we propose a Risk-Averse Certification framework for Bayesian neural networks called RAC-BNN. Our method leverages sampling and optimisation to compute a sound approximation of the output set of a BNN, represented using a set of template polytopes. To enhance robustness evaluation, we integrate a coherent distortion risk measure--Conditional Value at Risk (CVaR)--into the certification framework, providing probabilistic guarantees based on empirical distributions obtained through sampling. We validate RAC-BNN on a range of regression and classification benchmarks and compare its performance with a state-of-the-art method. The results show that RAC-BNN effectively quantifies robustness under worst-performing risky scenarios, and achieves tighter certified bounds and higher efficiency in complex tasks.