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

TL;DR

The paper addresses the vulnerability of random-walk (RW)-based decentralized learning to Pac-Man attacks, where a malicious node terminates visiting RWs to halt learning. It introduces Create-If-Late (CIL), a fully decentralized, self-regulating mechanism that creates new RWs when nodes go unvisited, thereby preventing RW extinction and enabling continued RW-SGD updates. The authors establish theoretical guarantees for no permanent extinction, almost-sure bounded RW populations, and convergence of RW-SGD to a surrogate minimizer $\tilde{\mathbf{x}}^*$ of $\tilde{f}(\mathbf{x})=\mathbb{E}_{u\sim\pi^{(\zeta)}_{\text{chain}}}[f_u(\mathbf{x})]$, including bias bounds and linear-time delay controls, and validate these results with extensive simulations on synthetic and MNIST datasets. The work demonstrates that resilience can be achieved without parameter estimation or global coordination, and provides practical insights into selecting creation parameters to bound the RW population while maintaining learning progress.

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.

Figures (40)

• Figure 1: An illustration of the Pac-Man attack: A malicious node (shown in red) intercepts and "eats" (terminates) any visiting RW with a positive probability. Despite behaving like a benign node to its neighbors, it prevents the random walk from continuing, leading to eventual extinction of all walks in the network.
• Figure 3: An example of a chain of RWs. When a benign node $u$ has not been visited for $A_u$ consecutive time slots, it creates a new RW (green). Similarly, when node $v$ has not been visited for $A_v$ time slots, it creates another new RW (orange). The blue trajectory connects these RWs and forms a chain.
• Figure 4: Loss v.s. learning steps on a complete graph: comparison between CIL and gossip-based SGD.
• Figure : (a) CIL and DecAFork
• Figure : (a) complete graph

Theorems & Definitions (41)

• Remark 1
• Remark 2
• Definition 1: Communication topologies and RWs
• Remark 3
• Definition 2: Timing conventions
• Definition 3
• Remark 4
• Definition 4: Robustly Connected Graph
• Remark 5
• Definition 5