Robust Distributed Optimization With Randomly Corrupted Gradients

TL;DR

This paper introduces a distributed optimization algorithm that is robust against arbitrary Byzantine failures, using a multi-layered defense mechanism and providing convergence guarantees for various cost functions.

Contribution

It presents the first provably robust distributed optimization method against Byzantine failures with no limit on the number of malicious agents.

Findings

The algorithm converges for strongly convex functions.

It guarantees convergence for smooth non-convex functions.

The method effectively mitigates Byzantine failures in distributed settings.

Abstract

In this paper, we propose a first-order distributed optimization algorithm that is provably robust to Byzantine failures-arbitrary and potentially adversarial behavior, where all the participating agents are prone to failure. We model each agent's state over time as a two-state Markov chain that indicates Byzantine or trustworthy behaviors at different time instants. We set no restrictions on the maximum number of Byzantine agents at any given time. We design our method based on three layers of defense: 1) temporal robust aggregation, 2) spatial robust aggregation, and 3) gradient normalization. We study two settings for stochastic optimization, namely Sample Average Approximation and Stochastic Approximation. We provide convergence guarantees of our method for strongly convex and smooth non-convex cost functions.