We investigate a novel approach to resilient distributed optimization with quadratic costs in a multi-agent system prone to unexpected events that make some agents misbehave. In contrast to commonly adopted filtering strategies, we draw inspiration from phenomena modeled through the Friedkin-Johnsen dynamics and argue that adding competition to the mix can improve resilience in the presence of misbehaving agents. Our intuition is corroborated by analytical and numerical results showing that (i) there exists a nontrivial trade-off between full collaboration and full competition and (ii) our competition-based approach can outperform state-of-the-art algorithms based on Weighted Mean Subsequence Reduced. We also study impact of communication topology and connectivity on resilience, pointing out insights to robust network design.

翻译：我们针对多智能体系统中因突发恶意行为引发的二次成本弹性分布式优化问题，提出了一种创新方法。与常用的滤波策略不同，我们从Friedkin-Johnsen动力学建模现象中汲取灵感，论证在系统中引入竞争机制可提升应对恶意智能体时的弹性。分析结果与数值实验均证实：（i）完全合作与完全竞争之间存在非平凡权衡关系；（ii）基于竞争的方法能超越基于加权均值子序列约减（Weighted Mean Subsequence Reduced）的先进算法。此外，我们研究了通信拓扑结构与连接性对弹性的影响，为鲁棒网络设计提供了关键见解。