Self-Healing First-Order Distributed Optimization

We describe 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.