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.

翻译：鉴于现实环境的固有复杂性和动态特性，引入风险度量对于深度学习模型的鲁棒性评估至关重要。本文提出一种面向贝叶斯神经网络的风险规避认证框架RAC-BNN。该方法通过采样与优化技术，计算贝叶斯神经网络输出集合的可靠近似表示，该集合采用模板多面体进行表征。为增强鲁棒性评估，我们将一致性失真风险度量——条件风险价值（CVaR）——整合至认证框架中，基于采样获得的经验分布提供概率保证。我们在系列回归与分类基准任务上验证RAC-BNN，并将其性能与前沿方法进行对比。实验结果表明，RAC-BNN能有效量化最劣风险情境下的鲁棒性，在复杂任务中实现了更紧致的认证边界和更高的计算效率。