Robustness of Iteratively Pre-Conditioned Gradient-Descent Method: The Case of Distributed Linear Regression Problem

TL;DR

This paper investigates the robustness of the Iteratively Pre-conditioned Gradient-descent (IPG) method for distributed linear regression in noisy multi-agent systems, demonstrating its favorable performance against state-of-the-art algorithms.

Contribution

It provides a comprehensive analysis of IPG's robustness to observation and process noise in distributed linear regression, which was not previously studied.

Findings

IPG method is robust against observation and process noise.

Empirical results show IPG outperforms other algorithms in noisy settings.

IPG converges faster than related methods in practical scenarios.

Abstract

This paper considers the problem of multi-agent distributed linear regression in the presence of system noises. In this problem, the system comprises multiple agents wherein each agent locally observes a set of data points, and the agents' goal is to compute a linear model that best fits the collective data points observed by all the agents. We consider a server-based distributed architecture where the agents interact with a common server to solve the problem; however, the server cannot access the agents' data points. We consider a practical scenario wherein the system either has observation noise, i.e., the data points observed by the agents are corrupted, or has process noise, i.e., the computations performed by the server and the agents are corrupted. In noise-free systems, the recently proposed distributed linear regression algorithm, named the Iteratively Pre-conditioned Gradient-descent (IPG) method, has been claimed to converge faster than related methods. In this paper, we study the robustness of the IPG method, against both the observation noise and the process noise. We empirically show that the robustness of the IPG method compares favorably to the state-of-the-art algorithms.