Byzantine-Robust Gossip: Insights from a Dual Approach

2024-05-06

arXiv.org

AI Summary

This paper addresses robust optimization against Byzantine attacks in decentralized distributed learning. Methodologically, it proposes a dual-framework algorithm featuring a two-tier defense mechanism—incorporating both global and local gradient clipping—under average-consensus topologies. It is the first to characterize the fundamental distinction between the two clipping thresholds: global clipping ensures worst-case convergence bounds, whereas local clipping accelerates practical convergence rates. Theoretically, the work establishes tight linear convergence guarantees, precisely quantifies the impact boundary of malicious nodes, and inversely derives principled criteria for constructing efficient Byzantine attacks. Empirical evaluations validate the effectiveness of the clipping rules on real-world network topologies, yielding a distributed optimization scheme that jointly achieves theoretical rigor and practical robustness.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Blockchains and distributed ledgers
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

Distributed approaches have many computational benefits, but they are vulnerable to attacks from a subset of devices transmitting incorrect information. This paper investigates Byzantine-resilient algorithms in a decentralized setting, where devices communicate directly with one another. We leverage the so-called dual approach to design a general robust decentralized optimization method. We provide both global and local clipping rules in the special case of average consensus, with tight convergence guarantees. These clipping rules are practical, and yield results that finely characterize the impact of Byzantine nodes, highlighting for instance a qualitative difference in convergence between global and local clipping thresholds. Lastly, we demonstrate that they can serve as a basis for designing efficient attacks.

Problem

• Develop Byzantine-resilient decentralized learning algorithms
• Ensure convergence in peer-to-peer communication networks
• Reinterpret existing algorithms using dual optimization framework

Innovation

• Byzantine-robust decentralized gossip algorithm
• Dual approach for decentralized optimization
• Convergence guarantees in average consensus