Self-Creating Random Walks for Decentralized Learning under Pac-Man Attacks

TL;DR

This paper introduces a decentralized learning algorithm resilient to Pac-Man attacks, which probabilistically terminate random walks, ensuring continued learning despite malicious nodes.

Contribution

The paper proposes the CREATE-IF-LATE (CIL) algorithm that enables self-creating RWs, preventing extinction and ensuring convergence under adversarial Pac-Man attacks.

Findings

CIL guarantees non-extinction of RWs

Ensures convergence of stochastic gradient descent

Maintains learning with at most linear delay

Abstract

Random walk (RW)-based algorithms have long been popular in distributed systems due to low overheads and scalability, with recent growing applications in decentralized learning. However, their reliance on local interactions makes them inherently vulnerable to malicious behavior. In this work, we investigate an adversarial threat that we term the ``Pac-Man'' attack, in which a malicious node probabilistically terminates any RW that visits it. This stealthy behavior gradually eliminates active RWs from the network, effectively halting the learning process without triggering failure alarms. To counter this threat, we propose the CREATE-IF-LATE (CIL) algorithm, which is a fully decentralized, resilient mechanism that enables self-creating RWs and prevents RW extinction in the presence of Pac-Man. Our theoretical analysis shows that the CIL algorithm guarantees several desirable properties, such as (i) non-extinction of the RW population, (ii) almost sure boundedness of the RW population, and (iii) convergence of RW-based stochastic gradient descent even in the presence of Pac-Man with a quantifiable deviation from the true optimum. Moreover, the learning process experiences at most a linear time delay due to Pac-Man interruptions and RW regeneration. Our extensive empirical results on both synthetic and public benchmark datasets validate our theoretical findings.