Convergence and Applications of a Gossip-based Gauss-Newton Algorithm

TL;DR

This paper introduces a distributed Gossip-based Gauss-Newton algorithm for non-linear least squares problems, demonstrating convergence and performance comparable to centralized methods, with robustness to network failures and advantages over first-order methods.

Contribution

It presents a novel multi-agent distributed Gauss-Newton algorithm with convergence analysis and practical performance benefits in non-convex optimization.

Findings

Achieves performance similar to centralized Gauss-Newton

Maintains robustness under network failures

Outperforms other distributed first-order methods

Abstract

The Gauss-Newton algorithm is a popular and efficient centralized method for solving non-linear least squares problems. In this paper, we propose a multi-agent distributed version of this algorithm, named Gossip-based Gauss-Newton (GGN) algorithm, which can be applied in general problems with non-convex objectives. Furthermore, we analyze and present sufficient conditions for its convergence and show numerically that the GGN algorithm achieves performance comparable to the centralized algorithm, with graceful degradation in case of network failures. More importantly, the GGN algorithm provides significant performance gains compared to other distributed first order methods.