Rohit Bhagat

Xingran Chen, Parimal Parag, Rohit Bhagat et al.

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.

Xingran Chen, Parimal Parag, Rohit Bhagat et al.

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 Average Crossing (AC) algorithm--a fully decentralized mechanism for duplicating RWs to prevent RW extinction in the presence of Pac-Man. Our theoretical analysis establishes that (i) the RW population remains almost surely bounded under AC and (ii) RW-based stochastic gradient descent remains convergent under AC, even in the presence of Pac-Man, with a quantifiable deviation from the true optimum. Our extensive empirical results on both synthetic and real-world datasets corroborate our theoretical findings. Furthermore, they uncover a phase transition in the extinction probability as a function of the duplication threshold. We offer theoretical insights by analyzing a simplified variant of the AC, which sheds light on the observed phase transition.