Self-Healing First-Order Distributed Optimization

TL;DR

This paper introduces a family of first-order distributed optimization algorithms that are robust and self-healing, maintaining correctness despite network changes, failures, and dynamic conditions, which is a novel achievement for single-Laplacian methods.

Contribution

The paper presents the first single-Laplacian distributed optimization algorithms that are self-healing and robust to various network disruptions and changes.

Findings

Algorithms guarantee correctness despite random initialization.

They remain effective despite agents dropping in or out.

They handle changing local cost functions and communication failures.

Abstract

In this paper 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 correctness is guaranteed even if they are initialized randomly, agents drop in or out of the network, local cost functions change, or communication packets are dropped. Our algorithms are the first single-Laplacian methods to exhibit all of these characteristics. We achieve self-healing by sacrificing internal stability, a fundamental trade-off for single-Laplacian methods.