This work focuses on the problem of distributed optimization in multi-agent cyberphysical systems, where a legitimate agents' iterates are 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, numerical results are presented that validate our analytical convergence guarantees even when the malicious agents compose the majority of agents in the network and where existing methods fail to converge to the optimal nominal points.

翻译：本文聚焦于多智能体信息物理系统中的分布式优化问题，其中合法智能体的迭代过程同时受到潜在恶意邻居智能体发送的值及其自身利己目标函数的影响。我们开发了一种新的算法与分析框架，针对智能体间存在可被利用的随机信任值的一类问题实现弹性。在此情况下，我们证明即使存在恶意智能体，系统仍能在均值和几乎必然意义下收敛至真实全局最优点。此外，我们以到最优值的期望平方距离上界形式提供了预期收敛速度保证。最后，通过数值结果验证了我们的分析收敛保证，即使在恶意智能体占网络多数且现有方法无法收敛至最优标称点的情况下依然有效。