Participation-Sensitive Convergence and the Fragment First, Converge Later Pattern in Asynchronous Online Learning: A Topological Analysis Across 22 OULAD Courses

Decentralised federated learning, based on peer-to-peer communication, is increasingly proposed for on-device training of machine learning models, promising a privacy-preserving, communication-efficient training process with no risk of single-point failure. However, the role of structural and temporal inhomogeneities in such fully decentralised settings remains poorly understood. Here, we investigate their effects when model parameters are locally averaged during aggregation. We show that the decentralised federated learning process is governed, both in the early phase and the late, stationary limit, by the same dynamics as a lazy random-walk diffusion process on temporal networks. Based on this mapping, we demonstrate that the typical experimental scenario used in decentralised federated learning leads to unrealistically rapid convergence because of ignoring the temporal and structural inhomogeneities inherent in the communication network. We analyse real-world temporal networks and find that inhomogeneities most often dramatically slow down diffusion, hence the convergence process.

Asynchronous federated learning improves scalability by updating the global model from a server-side buffer of client updates as they arrive, rather than waiting for all selected clients to finish. While efficient, this arrival-driven aggregation can silently distort representation learning under heterogeneous participation. We identify silent rarity failure, a hidden failure mode in which clients holding rare labels contribute too weakly to the global model even though its overall accuracy appears largely unaffected. This failure arises from two coupled effects: rare-label clients may submit updates less frequently when they are slower or less available, creating participation bias; and once their updates enter the buffer, standard asynchronous aggregation assigns them no compensating influence, creating aggregation bias. We propose FedRAW, a fully server-side aggregation method that preserves rare-label influence without changing local training, client objectives, or communication protocols. FedRAW combines client-level update deduplication, which prevents frequently arriving clients from repeatedly dominating the update buffer, with rare-label-aware weighting, which increases the influence of clients carrying low-coverage labels. We formalize silent rarity failure through participation and aggregation bias, and show that FedRAW increases rare-label client influence over uniform aggregation while preserving convergence. Across EMNIST Balanced, CIFAR-10, HAM10000, and ISIC-2019, FedRAW improves rarelabel accuracy while preserving comparable global accuracy and adding negligible server-side computation.

Online federated learning (OFL) has emerged as a popular framework for decentralized decision-making over continuous data streams without compromising client privacy. However, the adversary model assumed in standard OFL typically precludes any potential benefits of parallelization. Further, it fails to adequately capture the different sources of statistical variation in OFL problems. In this paper, we extend the OFL paradigm by integrating a stochastically extended adversary (SEA). Under this framework, the loss function remains fixed across clients over time. However, the adversary dynamically and independently selects the data distribution for each client at each time. We propose the \algoOFL{} algorithm to solve this problem, which utilizes online stochastic gradient descent at the clients, along with periodic global aggregation via the server. We establish bounds on the global network regret over a time horizon $T$ for two classes of functions: (1) for smooth and convex losses, we prove an $\mathcal{O}(\sqrt{T})$ bound, and (2) for smooth and strongly convex losses, we prove an $\mathcal{O}(\log T)$ bound. Through careful analysis, we quantify the individual impact of both spatial (across clients) and temporal (over time) data heterogeneity on the regret bounds. Consequently, we identify a regime of mild temporal variation (relative to stochastic gradient variance), where the network regret improves with parallelization. Hence, in the SEA setting, our results improve the existing pessimistic worst-case results in online federated learning.