Tight Stability Bounds for Robust Distributed Learning: Byzantine Failures Hurt Generalization More than Data Poisoning

Abstract

Robust distributed learning algorithms aim to maintain reliable performance despite the presence of misbehaving workers. Such misbehaviors are commonly modeled as *Byzantine failures*, allowing arbitrarily corrupted communication, or as *data poisoning*, a weaker form of corruption restricted to local training data. While prior work shows similar optimization guarantees for both models, an important question remains: *How do these threat models impact generalization?* We show, for the first time, a fundamental gap in generalization guarantees between the two threat models: Byzantine failures yield strictly worse rates than those achievable under data poisoning. Our findings leverage a tight algorithmic stability analysis of robust distributed learning. Specifically, we prove that: *(i)* under data poisoning, the uniform algorithmic stability of an algorithm with optimal optimization guarantees degrades by an additive factor of $\varTheta ( \frac{f}{n-f} )$, with $f$ out of $n$ workers misbehaving; whereas *(ii)* under Byzantine failures, the degradation is in $\Omega \big( \sqrt{ \frac{f}{n-2f}} \big)$.