Distributed approaches have many computational benefits, but they are vulnerable to attacks from a subset of devices transmitting incorrect information. This paper investigates Byzantine-resilient algorithms in a decentralized setting, where devices communicate directly with one another. We leverage the so-called dual approach to design a general robust decentralized optimization method. We provide both global and local clipping rules in the special case of average consensus, with tight convergence guarantees. These clipping rules are practical, and yield results that finely characterize the impact of Byzantine nodes, highlighting for instance a qualitative difference in convergence between global and local clipping thresholds. Lastly, we demonstrate that they can serve as a basis for designing efficient attacks.

翻译：分布式方法具有许多计算优势，但易受部分设备传输错误信息的攻击。本文研究去中心化环境下的拜占庭容错算法，其中设备直接相互通信。我们利用所谓的对偶方法设计了一种通用的鲁棒去中心化优化方法。在平均共识的特殊情况下，我们提供了全局和局部裁剪规则，并给出了严格的收敛保证。这些裁剪规则具有实用性，其结果精细地刻画了拜占庭节点的影响，例如突显了全局与局部裁剪阈值在收敛性上的定性差异。最后，我们证明这些规则可作为设计高效攻击的基础。