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This research exposes a critical misalignment between Wasserstein distributionally robust optimization (WDRO) risk metrics and actual robust accuracy when using standard loss functions like cross-entropy. The authors introduce Wasserstein distributional attacks (WDA) with an optimized support-search algorithm that directly evaluates adversarial performance, demonstrating superior efficacy on major benchmarks. This work is essential for practitioners seeking reliable methods to assess model resilience against distributional shifts without relying on flawed surrogate losses.
Wasserstein Robust Classification Error: Surrogate Loss Misalignment and Distributional Attacks
arXiv:2510.10000v3 Announce Type: replace Abstract: Wasserstein distributionally robust optimization (WDRO) provides a framework for evaluating model robustness through the worst-case expectation in the Wasserstein ball around a reference distribution. We prove that ordering hypotheses by increasing WDRO risk is equivalent to ordering them by decreasing robust accuracy if and only if the loss function is a positive multiple of the zero-one loss plus a label-dependent offset. For a class of loss functions including cross-entropy, we show that a hypothesis with perfect robust accuracy can conversely have a higher WDRO risk than another hypothesis with near zero robust accuracy. To evaluate robust accuracy directly, we develop Wasserstein distributional attacks (WDA), which add a weight generation stage after candidate support search to optimize the allocation of empirical mass under the Wasserstein constraint, rather than assigning each data point's full mass to one returned attack point as existing methods do. We further introduce a support-search algorithm for WDA that finds nearby misclassified inputs. On CIFAR-10, CIFAR-100, and ImageNet, WDA using our search algorithm achieves the lowest adversarial accuracy in most tested settings. Our code is available at https://github.com/OLab-Repo/WDA.
Abstract:Wasserstein distributionally robust optimization (WDRO) provides a framework for evaluating model robustness through the worst-case expectation in the Wasserstein ball around a reference distribution. We prove that ordering hypotheses by increasing WDRO risk is equivalent to ordering them by decreasing robust accuracy if and only if the loss function is a positive multiple of the zero-one loss plus a label-dependent offset. For a class of loss functions including cross-entropy, we show that a hypothesis with perfect robust accuracy can conversely have a higher WDRO risk than another hypothesis with near zero robust accuracy. To evaluate robust accuracy directly, we develop Wasserstein distributional attacks (WDA), which add a weight generation stage after candidate support search to optimize the allocation of empirical mass under the Wasserstein constraint, rather than assigning each data point's full mass to one returned attack point as existing methods do. We further introduce a support-search algorithm for WDA that finds nearby misclassified inputs. On CIFAR-10, CIFAR-100, and ImageNet, WDA using our search algorithm achieves the lowest adversarial accuracy in most tested settings. Our code is available at this https URL.
Machine Learning (cs.LG); Optimization and Control (math.OC); Machine Learning (stat.ML)
arXiv:2510.10000 [cs.LG]
(or arXiv:2510.10000v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2510.10000 Focus to learn more arXiv-issued DOI via DataCite
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