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：我们研究了一种新颖的弹性分布式优化方法，针对具有二次成本的多智能体系统，该系统易受意外事件影响而导致部分智能体行为失当。与常见的过滤策略不同，我们从Friedkin-Johnsen动力学建模的现象中汲取灵感，论证在系统中引入竞争机制可提升存在不良行为智能体时的弹性。理论与数值分析结果佐证了我们的直觉：（i）完全协作与完全竞争之间存在非平凡权衡；（ii）基于竞争的方法可超越基于加权均值子序列缩减（Weighted Mean Subsequence Reduced）的最先进算法。此外，我们还研究了通信拓扑结构与连通性对弹性的影响，为鲁棒网络设计提供了关键见解。