In decentralized machine learning, different devices communicate in a peer-to-peer manner to collaboratively learn from each other's data. Such approaches are vulnerable to misbehaving (or Byzantine) devices. We introduce $\mathrm{F}\text{-}\rm RG$, a general framework for building robust decentralized algorithms with guarantees arising from robust-sum-like aggregation rules $\mathrm{F}$. We then investigate the notion of *breakdown point*, and show an upper bound on the number of adversaries that decentralized algorithms can tolerate. We introduce a practical robust aggregation rule, coined $\rm CS_{ours}$, such that $\rm CS_{ours}\text{-}RG$ has a near-optimal breakdown. Other choices of aggregation rules lead to existing algorithms such as $\rm ClippedGossip$ or $\rm NNA$. We give experimental evidence to validate the effectiveness of $\rm CS_{ours}\text{-}RG$ and highlight the gap with $\mathrm{NNA}$, in particular against a novel attack tailored to decentralized communications.

翻译：在去中心化机器学习中，不同设备以点对点方式进行通信，以协作学习彼此的数据。此类方法易受恶意（或拜占庭）设备的影响。我们引入了$\mathrm{F}\text{-}\rm RG$，这是一个用于构建鲁棒去中心化算法的通用框架，其保证源于类鲁棒和聚合规则$\mathrm{F}$。随后，我们研究了*崩溃点*的概念，并给出了去中心化算法所能容忍的对抗者数量的上界。我们引入了一种实用的鲁棒聚合规则，命名为$\rm CS_{ours}$，使得$\rm CS_{ours}\text{-}RG$具有接近最优的崩溃点。其他聚合规则的选择则引出了现有算法，如$\rm ClippedGossip$或$\rm NNA$。我们通过实验证据验证了$\rm CS_{ours}\text{-}RG$的有效性，并强调了其与$\mathrm{NNA}$之间的差距，特别是在针对一种专为去中心化通信设计的新型攻击时。