Practical Validity Conditions for Byzantine-Tolerant Federated Learning
实用的拜占庭容错联邦学习有效性条件
Mélanie Cambus, Darya Melnyk, Tijana Milentijević, Stefan Schmid
AI总结 本文提出最小包围球有效性条件及其放松形式c-MEB有效性,为联邦学习提供更实用的有效性保障,适用于多数客户端诚实的情况,并与传统有效性条件建立联系。
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鲁棒聚合是拜占庭容错联邦学习的核心操作。为了确保聚合质量不依赖数据分布或攻击,需要有效性条件。它们提供了聚合输出必须位于的几何保证。广泛使用的凸有效性要求输出位于诚实向量的凸包内。尽管这种保证在理论上很强,但并不适合现代联邦学习系统,因为它有维度依赖的容错性和排除了许多实际聚合规则。我们引入了最小包围球(MEB)有效性条件及其实松形式c-MEB有效性,其中c是一个常数。我们证明精确MEB有效性仍受有限容错性的限制,而放松的c-MEB有效性在多数客户端诚实的情况下(即n>2t)可以实现。我们为放松条件给出了最优的MinMax-MEB规则,具有c<√2的界,并证明了标准聚合器(包括最小直径平均、中位数和几何中位数)的显式放松MEB保证。最后,我们将MEB有效性与先前文献中研究的凸、放松凸和盒有效性联系起来,从而为拜占庭鲁棒聚合提供了系统的几何有效性条件图谱。我们的结果表明,放松的MEB有效性连接了分布式计算中的有效性条件和拜占庭容错聚合规则,并提供了一个实用的替代方案,替代凸有效性。
Robust aggregation is the core operation in Byzantine-tolerant federated learning. To ensure the quality of aggregation independently of data distribution or attacks, validity conditions are needed. They provide geometric guarantees of where the output of the aggregation must lie. The widespread convex validity requires the output to lie in the convex hull of the honest vectors. Although this guarantee is strong in theory, it is poorly suited to modern federated learning systems, as it has dimension-dependent resilience and excludes many practical aggregation rules. We introduce the minimum enclosing ball (MEB) validity condition for robust aggregation, as well as its multiplicative relaxation, $c$-MEB validity, where $c$ is a constant. We show that exact MEB validity still suffers from limited resilience, while relaxed $c$-MEB validity is achievable if a majority of clients is honest, i.e. $n>2t$. We give an optimal MinMax-MEB rule for the relaxed condition with the bound $c<\sqrt{2}$ and prove explicit relaxed-MEB guarantees for standard aggregators including minimum-diameter averaging, medoid and geometric median. Finally, we relate MEB validity to convex, relaxed-convex and box validity studied in prior literature, thus providing a systematic map of geometric validity conditions for Byzantine-robust aggregation. Our results show that relaxed MEB validity connects validity conditions in distributed computing and Byzantine-tolerant aggregation rules, and offers a practical alternative to convex validity.