We focus on learning adversarially robust classifiers under a cost-sensitive scenario, where the potential harm of different classwise adversarial transformations is encoded in a binary cost matrix. Existing methods are either empirical that cannot certify robustness or suffer from inherent scalability issues. In this work, we study whether randomized smoothing, a more scalable robustness certification framework, can be leveraged to certify cost-sensitive robustness. Built upon a notion of cost-sensitive certified radius, we show how to adapt the standard randomized smoothing certification pipeline to produce tight robustness guarantees for any cost matrix. In addition, with fine-grained certified radius optimization schemes specifically designed for different data subgroups, we propose an algorithm to train smoothed classifiers that are optimized for cost-sensitive robustness. Extensive experiments on image benchmarks and a real-world medical dataset demonstrate the superiority of our method in achieving significantly improved performance of certified cost-sensitive robustness while having a negligible impact on overall accuracy.

我们研究了在成本敏感场景中学习对抗鲁棒分类器的问题，通过一个二进制成本矩阵编码不同分类的敌对转换的潜在危害。我们提出了一种能够为任意成本矩阵提供严密鲁棒性保证的改进版随机平滑认证方法，并使用针对不同数据子组的细粒度认证半径优化方案，提出了一种优化成本敏感鲁棒性的平滑分类器训练算法。我们在图像基准测试和现实世界医学数据集上的大量实验证明了我们方法在实现显著改善认证成本敏感鲁棒性性能的同时，对整体准确性的影响可以忽略不计。

通过随机平滑实现可证明稳健的代价敏感学习