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.

翻译：基于随机游走（RW）的算法因其低开销和可扩展性，在分布式系统中长期受到青睐，近年来在去中心化学习中的应用日益增长。然而，这类算法对局部交互的依赖使其本质上易受恶意行为影响。本文研究一种我们称之为“Pac-Man”攻击的对抗性威胁，其中恶意节点以一定概率终止任何访问它的随机游走。这种隐蔽行为会逐渐从网络中清除活跃的随机游走，从而有效中止学习过程且不触发故障警报。为应对此威胁，我们提出CREATE-IF-LATE（CIL）算法，这是一种完全去中心化的弹性机制，能够实现随机游走的自创生，并在Pac-Man攻击存在时防止随机游走灭绝。我们的理论分析表明，CIL算法保证以下理想特性：（i）随机游走种群不灭绝，（ii）随机游走种群几乎必然有界，以及（iii）即使在存在Pac-Man攻击的情况下，基于随机游走的随机梯度下降仍能收敛，且与真实最优解的偏差可量化。此外，由于Pac-Man中断和随机游走再生，学习过程至多经历线性时间延迟。我们在合成数据集和公共基准数据集上的大量实验结果验证了理论结论。