论文标题
Wasserstein的原则性学习方法在局部扰动中优化了强大的优化
Principled learning method for Wasserstein distributionally robust optimization with local perturbations
论文作者
论文摘要
Wasserstein分布在强大的优化方面（WDRO）试图学习一个模型，以最大程度地减少Wasserstein Ball定义的经验数据分布附近的局部最坏风险。自从引入以来，尽管WDRO已被关注为有前途的推断工具，但其理论理解尚未完全成熟。 Gao等。 （2017年）提出了一个最小化器，基于当地最坏情况风险的可拖动近似值，但没有显示风险一致性。在本文中，我们提出了一个基于新型近似定理的最小化器，并提供相应的风险一致性结果。此外，我们为特殊情况（Zhang et al。，2017）开发了局部扰动数据的WDRO推断。我们表明，我们的近似和风险一致性自然扩展到数据局部扰动的情况。数值实验证明了使用图像分类数据集的提议方法的鲁棒性。我们的结果表明，所提出的方法的精度明显高于嘈杂数据集上的基线模型。
Wasserstein distributionally robust optimization (WDRO) attempts to learn a model that minimizes the local worst-case risk in the vicinity of the empirical data distribution defined by Wasserstein ball. While WDRO has received attention as a promising tool for inference since its introduction, its theoretical understanding has not been fully matured. Gao et al. (2017) proposed a minimizer based on a tractable approximation of the local worst-case risk, but without showing risk consistency. In this paper, we propose a minimizer based on a novel approximation theorem and provide the corresponding risk consistency results. Furthermore, we develop WDRO inference for locally perturbed data that include the Mixup (Zhang et al., 2017) as a special case. We show that our approximation and risk consistency results naturally extend to the cases when data are locally perturbed. Numerical experiments demonstrate robustness of the proposed method using image classification datasets. Our results show that the proposed method achieves significantly higher accuracy than baseline models on noisy datasets.
