Election Coding for Distributed Learning: Protecting SignSGD against Byzantine Attacks

TL;DR

This paper introduces Election Coding, a coding-theoretic framework that enhances SignSGD's robustness against Byzantine failures in distributed learning, ensuring accurate majority voting with minimal communication overhead.

Contribution

It develops new coding schemes, including Bernoulli and deterministic algebraic codes, to tolerate Byzantine attacks and establishes theoretical bounds on their performance.

Findings

Bernoulli codes have bounded error probability in majority estimation.

Deterministic codes can perfectly tolerate Byzantine failures.

Experimental results confirm Byzantine robustness in deep learning tasks.

Abstract

Recent advances in large-scale distributed learning algorithms have enabled communication-efficient training via SignSGD. Unfortunately, a major issue continues to plague distributed learning: namely, Byzantine failures may incur serious degradation in learning accuracy. This paper proposes Election Coding, a coding-theoretic framework to guarantee Byzantine-robustness for SignSGD with Majority Vote, which uses minimum worker-master communication in both directions. The suggested framework explores new information-theoretic limits of finding the majority opinion when some workers could be malicious, and paves the road to implement robust and efficient distributed learning algorithms. Under this framework, we construct two types of explicit codes, random Bernoulli codes and deterministic algebraic codes, that can tolerate Byzantine attacks with a controlled amount of computational redundancy. For the Bernoulli codes, we provide upper bounds on the error probability in estimating the majority opinion, which give useful insights into code design for tolerating Byzantine attacks. As for deterministic codes, we construct an explicit code which perfectly tolerates Byzantines, and provide tight upper/lower bounds on the minimum required computational redundancy. Finally, the Byzantine-tolerance of the suggested coding schemes is confirmed by deep learning experiments on Amazon EC2 using Python with MPI4py package.