Self-Healing First-Order Distributed Optimization with Packet Loss

TL;DR

This paper introduces SH-SVL, a family of distributed optimization algorithms that are resilient to network changes, agent dynamics, and packet loss, ensuring convergence under various disruptions.

Contribution

The paper presents the first single-Laplacian distributed convex optimization methods with self-healing capabilities for network and communication failures.

Findings

Algorithms guarantee convergence despite random initialization.

Effective in scenarios with agents joining or leaving.

Resilient to dropped communication packets in simulations.

Abstract

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.