Randomized Kaczmarz in Adversarial Distributed Setting

SIAM Journal on Scientific Computing, Volume 46, Issue 3, Page B354-B376, June 2024.
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. In this paper, we propose an iterative approach that is adversary-tolerant for convex optimization problems. By leveraging simple statistics, our method ensures convergence and is capable of adapting to adversarial distributions. Additionally, the efficiency of the proposed methods for solving convex problems is shown in simulations with the presence of adversaries. Through simulations, we demonstrate the efficiency of our approach in the presence of adversaries and its ability to identify adversarial workers with high accuracy and tolerate varying levels of adversary rates.