# Random Walk Learning and the Pac-Man Attack

arXiv: https://arxiv.org/abs/2508.05663 · HTML: https://mlsanity.com/paper/2508.05663/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 41 references that are in the map.
- First posted on arXiv 1 Aug 2025.

## Builds on (most cited first, 10 of 10)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Measuring the Effects of Non-Identical Data Distribution for Federated Visual Classification](https://mlsanity.com/paper/1909.06335/) (2019)
- [A Unified Theory of Decentralized SGD with Changing Topology and Local Updates](https://mlsanity.com/paper/2003.10422/) (2020)
- [On Markov Chain Gradient Descent](https://mlsanity.com/paper/1809.04216/) (2018)
- [Stochastic Gradient Descent under Markovian Sampling Schemes](https://mlsanity.com/paper/2302.14428/) (2023)
- [Walkman: A Communication-Efficient Random-Walk Algorithm for Decentralized Optimization](https://mlsanity.com/paper/1804.06568/) (2018)
- [Walk for Learning: A Random Walk Approach for Federated Learning from Heterogeneous Data](https://mlsanity.com/paper/2206.00737/) (2022)
- [The Entrapment Problem in Random Walk Decentralized Learning](https://mlsanity.com/paper/2407.20611/) (2024)
- [Coupled-Space Attacks against Random-Walk-based Anomaly Detection](https://mlsanity.com/paper/2307.14387/) (2023)
- [Self-Regulating Random Walks for Resilient Decentralized Learning on Graphs](https://mlsanity.com/paper/2407.11762/) (2024)

## Built on by (most cited first, 3 of 3)

- [Self-Creating Random Walks for Decentralized Learning under Pac-Man Attacks](https://mlsanity.com/paper/2601.07674/) (2026)
- [RW-LoRA: Communication-Efficient Decentralized LoRA Fine-Tuning via Random Walks](https://mlsanity.com/paper/2609.00078/) (2026)
- [Multi-Token Random-Walk Learning via Meeting-Triggered Information Exchange](https://mlsanity.com/paper/2610.14716/) (2026)

## Abstract (arXiv)

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.