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

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.

Decentralized learning enhances privacy, scalability, and fault tolerance by distributing data and computation across nodes. A popular approach is Federated learning, which relies on a central aggregator, yet faces challenges such as server vulnerabilities, scalability issues, privacy risks and most importantly, the single point of failure. Alternatively Gossip Learning and Epidemic Learning offer fully decentralization through peer-to-peer exchanges of model updates, ensuring robustness and privacy, at the price of slower model convergence. In this work, we introduce a novel decentralized learning framework called HEAL. HEAL is the first cross-layer decentralized learning framework that exploits an optimized self-organizing and self-healing underlying P2P overlay combining the strengths of Federated Learning, Gossip and Epidemic Learning. Leveraging the recently proposed Elevator algorithm, HEAL promotes dynamically chosen nodes to act as aggregators. Through simulations, we demonstrate that HEAL has similar performances to that of Federated Learning in crash-free settings, while being fully decentralized and fault-tolerant. In crash and churn prone environments HEAL outperforms Gossip and Epidemic Learning.

Reachability is the most fundamental logical objective, yet it is notoriously difficult to learn in reinforcement learning settings: even for Markov decision processes, PAC learning of reachability is impossible without additional assumptions. This difficulty also holds in turn-based stochastic games (TBSGs), where two adversarial players interact on a finite state space. In this work, we consider turn-based stochastic games with reachability objectives. For such settings, adversarial learning, in which players are adversarial even in the learning phase, is impossible. Therefore, the goal is to consider learning, in which both players learn the unknown model together. In this spirit, previous literature on PAC learning in TBSGs considers (a)~public information shared by both players; and (b)~centralized learning, which means that players share the same learning algorithm. In this work, our contribution is two-fold. First, we relax these strong assumptions and ensure learning: (i)~with private information not shared with the other player; and (ii)~decentralized learning where the players do not share the same learning algorithm. To the best of our knowledge, this work is the first positive result for decentralized and private information learning of TBSGs with reachability objectives. Second, we introduce a game-theoretic generalization of the Expected Conditional Distance (ECD) parameter, which measures the expected length of reaching the target set. We establish a polynomial-sample complexity bound with respect to the number of states, actions, ECD parameter, and inverses of error tolerance and failure probability.