联邦学习中提升分类鲁棒性，应对数据分布不确定性
FDR-SVM: A Federated Distributionally Robust Support Vector Machine via a Mixture of Wasserstein Balls Ambiguity Set
- 用混合沃瑟斯坦球构建新型不确定集，适配分布式数据特性
- 理论证明分类边界可分性，算法收敛且时间复杂度可控
- 在工业数据与UCI数据上显著优于现有先进方法
我们研究一个由多个客户端和中心服务器组成的联邦分类问题，其中每个客户端的本地数据保持私密，并且特征与标签均存在不确定性。为应对这些不确定性，我们提出一种新型联邦分布鲁棒支持向量机（FDR-SVM），使分类边界对本地数据分布扰动具有鲁棒性。每个客户端的数据服从未知的真实分布。为处理这种异质性，我们设计了一种新颖的混合沃瑟斯坦球（MoWB）不确定集，自然扩展了经典沃瑟斯坦球至联邦设置。我们建立了所提MoWB的理论保证，推导出泛化性能界，并证明其设计保持了FDR-SVM优化问题的可分性。随后，我们严格推导出两种求解FDR-SVM问题的算法，并分析其收敛行为及最坏情况时间复杂度。我们在工业数据和多个UCI数据集上评估了算法，结果表明其通常显著优于现有最先进方法。
原文摘要 · Abstract (English)
We study a federated classification problem over a network of multiple clients and a central server, in which each client's local data remains private and is subject to uncertainty in both the features and labels. To address these uncertainties, we develop a novel Federated Distributionally Robust Support Vector Machine (FDR-SVM), robustifying the classification boundary against perturbations in local data distributions. Specifically, the data at each client is governed by a unique true distribution that is unknown. To handle this heterogeneity, we develop a novel Mixture of Wasserstein Balls (MoWB) ambiguity set, naturally extending the classical Wasserstein ball to the federated setting. We then establish theoretical guarantees for our proposed MoWB, deriving an out-of-sample performance bound and showing that its design preserves the separability of the FDR-SVM optimization problem. Next, we rigorously derive two algorithms that solve the FDR-SVM problem and analyze their convergence behavior as well as their worst-case time complexity. We evaluate our algorithms on industrial data and various UCI datasets, whereby we demonstrate that they frequently outperform existing state-of-the-art approaches.
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