We describe SH-SVL, a parameterized family of first-order distributed optimization algorithms that enable a network of agents to collaboratively calculate a decision variable that minimizes the sum of cost functions at each agent. These algorithms are self-healing in that their convergence to the correct optimizer can be guaranteed even if they are initialized randomly, agents join or leave the network, or local cost functions change. We also present simulation evidence that our algorithms are self-healing in the case of dropped communication packets. Our algorithms are the first single-Laplacian methods for distributed convex optimization to exhibit all of these characteristics. We achieve self-healing by sacrificing internal stability, a fundamental trade-off for single-Laplacian methods.

翻译：我们提出SH-SVL这一参数化的一阶分布式优化算法族，使智能体网络能够协作计算使各智能体成本函数之和最小化的决策变量。这些算法具有自愈特性：即使初始化随机、智能体加入或离开网络、或局部成本函数发生变化，仍能保证收敛至正确最优解。我们还提供仿真证据表明，算法在通信数据包丢失情况下仍保持自愈能力。本算法是首个同时具备上述所有特性的单拉普拉斯分布式凸优化方法。我们通过牺牲内部稳定性实现自愈能力，这是单拉普拉斯方法需权衡的基本特性。