FedSEA: Achieving Benefit of Parallelization in Federated Online Learning

TL;DR

FedSEA introduces a novel federated online learning framework with a stochastic adversary, enabling parallelization benefits and improved regret bounds under certain data variation regimes.

Contribution

This paper extends OFL by modeling a stochastic adversary, proposing the FedSEA algorithm, and analyzing regret bounds that reveal conditions for parallelization advantages.

Findings

Regret bounds of ((T)) for convex losses.

Regret bounds of ((T)) for strongly convex losses.

Parallelization improves regret in regimes of mild temporal variation.

Abstract

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.