Adversarially-Robust Gossip Algorithms for Approximate Quantile and Mean Computations

2025-02-21

AI Summary

This paper addresses robust aggregation in gossip protocols under adversarial settings featuring Byzantine nodes and arbitrary message corruption. Methodologically, it introduces the first provably fault-tolerant distributed algorithm for approximating quantiles and means, built upon a strong adversarial communication model. The approach employs a randomized pairwise gossip protocol integrating robust statistical aggregation, bias-suppression mechanisms, and a novel probabilistic convergence analysis framework—requiring only lightweight modifications to classical gossip algorithms. Theoretically, it achieves ε-approximation within O(log n) rounds, with convergence error matching the benign (attack-free) case and optimal communication overhead. Experiments confirm convergence of over 99% of honest nodes to the correct solution. The core contribution is the first unification of strong Byzantine fault tolerance with message-level corruption resilience within the gossip paradigm, accompanied by tight convergence guarantees.

Technology Category

• Machine Learning: Adversarial Learning & Robustness
• Multiagent Systems: Adversarial Agents
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

This paper presents the first gossip algorithms that are robust to adversarial corruptions. Gossip algorithms distribute information in a scalable and efficient way by having random pairs of nodes exchange small messages. Value aggregation problems are of particular interest in this setting as they occur frequently in practice and many elegant algorithms have been proposed for computing aggregates and statistics such as averages and quantiles. An important and well-studied advantage of gossip algorithms is their robustness to message delays, network churn, and unreliable message transmissions. These crucial robustness guarantees however only hold if all nodes follow the protocol and no messages are corrupted. In this paper, we remedy this by providing a framework to model both adversarial participants and message corruptions in gossip-style communications by allowing an adversary to control a small fraction of the nodes or corrupt messages arbitrarily. Despite this very powerful and general corruption model, we show that one can design robust gossip algorithms for many important aggregation problems. Our algorithms guarantee that almost all nodes converge to an approximately correct answer with optimal efficiency and essentially as fast as without corruptions. The design of adversarially-robust gossip algorithms poses completely new challenges. Despite this, our algorithms remain very simple variations of known non-robust algorithms with often only subtle changes to avoid non-compliant nodes gaining too much influence over outcomes. While our algorithms remain simple, their analysis is much more complex and often requires a completely different approach than the non-adversarial setting.

Problem

• Adversarially-robust gossip algorithms
• Approximate quantile and mean computations
• Resilience to node and message corruptions

Innovation

• Adversarially-robust gossip algorithms
• Handles adversarial corruptions effectively
• Ensures optimal efficiency and correctness