Generalization Error Matters in Decentralized Learning Under Byzantine Attacks

TL;DR

This paper analyzes how Byzantine attacks affect the generalization errors in decentralized learning, revealing that such errors persist regardless of training sample size, which is critical for real-world applications.

Contribution

First analysis of generalization errors in Byzantine-resilient decentralized SGD algorithms, highlighting persistent errors caused by malicious agents.

Findings

Generalization errors cannot be fully eliminated due to Byzantine agents.

Theoretical analysis confirms persistent errors even with infinite data.

Numerical experiments validate the theoretical results.

Abstract

Recently, decentralized learning has emerged as a popular peer-to-peer signal and information processing paradigm that enables model training across geographically distributed agents in a scalable manner, without the presence of any central server. When some of the agents are malicious (also termed as Byzantine), resilient decentralized learning algorithms are able to limit the impact of these Byzantine agents without knowing their number and identities, and have guaranteed optimization errors. However, analysis of the generalization errors, which are critical to implementations of the trained models, is still lacking. In this paper, we provide the first analysis of the generalization errors for a class of popular Byzantine-resilient decentralized stochastic gradient descent (DSGD) algorithms. Our theoretical results reveal that the generalization errors cannot be entirely eliminated because of the presence of the Byzantine agents, even if the number of training samples are infinitely large. Numerical experiments are conducted to confirm our theoretical results.