Distributed Multiple Testing with False Discovery Rate Control in the Presence of Byzantines

TL;DR

This paper investigates how Byzantine attacks impact distributed multiple testing procedures controlling the false discovery rate, proposing analysis and countermeasures to maintain statistical integrity under adversarial conditions.

Contribution

It introduces a comprehensive analysis of Byzantine attack effects on FDR control in distributed testing and proposes strategies to mitigate these attacks.

Findings

Byzantine attacks can significantly inflate FDR in distributed testing.

Counter-attack strategies can effectively reduce the impact of Byzantine nodes.

Simulation results validate theoretical analysis and reveal trade-offs in attack and defense mechanisms.

Abstract

This work studies distributed multiple testing with false discovery rate (FDR) control in the presence of Byzantine attacks, where an adversary captures a fraction of the nodes and corrupts their reported p-values. We focus on two baseline attack models: an oracle model with the full knowledge of which hypotheses are true nulls, and a practical attack model that leverages the Benjamini-Hochberg (BH) procedure locally to classify which p-values follow the true null hypotheses. We provide a thorough characterization of how both attack models affect the global FDR, which in turn motivates counter-attack strategies and stronger attack models. Our extensive simulation studies confirm the theoretical results, highlight key design trade-offs under attacks and countermeasures, and provide insights into more sophisticated attacks.