Distributed randomized Kaczmarz for the adversarial workers

TL;DR

This paper introduces a distributed randomized Kaczmarz algorithm that is robust against adversarial or corrupted workers, ensuring convergence and accurate identification of adversaries in large-scale least-squares problems.

Contribution

The paper presents a novel adversary-tolerant iterative method for distributed least-squares problems that uses simple statistics to guarantee convergence and detect adversarial workers.

Findings

Algorithm converges in the presence of adversaries

High accuracy in identifying erroneous workers

Effective in various adversary rate scenarios

Abstract

Developing large-scale distributed methods that are robust to the presence of adversarial or corrupted workers is an important part of making such methods practical for real-world problems. Here, we propose an iterative approach that is adversary-tolerant for least-squares problems. The algorithm utilizes simple statistics to guarantee convergence and is capable of learning the adversarial distributions. Additionally, the efficiency of the proposed method is shown in simulations in the presence of adversaries. The results demonstrate the great capability of such methods to tolerate different levels of adversary rates and to identify the erroneous workers with high accuracy.