Enhancing resilience in distributed networks in the face of malicious agents is an important problem for which many key theoretical results and applications require further development and characterization. This work focuses on the problem of distributed optimization in multi-agent cyberphysical systems, where a legitimate agent's dynamic is influenced both by the values it receives from potentially malicious neighboring agents, and by its own self-serving target function. We develop a new algorithmic and analytical framework to achieve resilience for the class of problems where stochastic values of trust between agents exist and can be exploited. In this case we show that convergence to the true global optimal point can be recovered, both in mean and almost surely, even in the presence of malicious agents. Furthermore, we provide expected convergence rate guarantees in the form of upper bounds on the expected squared distance to the optimal value. Finally, we present numerical results that validate the analytical convergence guarantees we present in this paper even when the malicious agents compose the majority of agents in the network.
翻译:面对恶意物剂,加强分布式网络的复原力是一个重要的问题,许多关键的理论结果和应用都需要进一步发展和定性,这项工作的重点是多试剂网络物理系统中的分布优化问题,在这种系统中,合法物剂的动态受到潜在恶意邻居代理人的价值观的影响,也受到其自身为自己谋利的目标功能的影响。我们开发了新的算法和分析框架,以便在存在和可以利用代理人之间信任的随机价值的各类问题中实现复原力。在这种情况下,我们表明,即使在恶意物剂存在的情况下,也可以以平均值和几乎肯定的方式恢复与真正的全球最佳点的趋同。此外,我们还以预期平方距离至最佳价值的上限的形式提供预期汇合率保证。最后,我们提出了数字结果,以证实我们在本文中提出的分析趋同保证,即使恶意物剂构成网络中的大多数代理人。