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

Provably Robust Cost-Sensitive Learning via Randomized Smoothing

Several recent works have developed methods for training classifiers that are
certifiably robust against norm-bounded adversarial perturbations. These
methods assume that all the adversarial transformations are equally important,
which is seldom the case in real-world applications. We advocate for
cost-sensitive robustness as the criteria for measuring the classifier's
performance for tasks where some adversarial transformation are more important
than others. We encode the potential harm of each adversarial transformation in
a cost matrix, and propose a general objective function to adapt the robust
training method of Wong & Kolter (2018) to optimize for cost-sensitive
robustness. Our experiments on simple MNIST and CIFAR10 models with a variety
of cost matrices show that the proposed approach can produce models with
substantially reduced cost-sensitive robust error, while maintaining
classification accuracy.

本文研究了在实际应用中，某些对抗变换的重要性可能比其他变换更高的情况下，如何衡量分类器在对抗干扰下的鲁棒性，并提出了一般性的目标函数，将 Wong 和 Kolter（2018）的鲁棒训练方法进行了改进。通过实验证明，所提出的方法可以显著降低成本敏感鲁棒错误，同时保持分类准确性。