Decentralized Domain Generalization with Style Sharing: Formal Model and Convergence Analysis

Much of federated learning (FL) focuses on settings where local dataset statistics remain the same between training and testing. However, this assumption often does not hold in practice due to distribution shifts, motivating the development of domain generalization (DG) approaches that leverage source domain data to train models capable of generalizing to unseen target domains. In this paper, we are motivated by two major gaps in existing work on FL and DG: (1) the lack of formal mathematical analysis of DG objectives; and (2) DG research in FL being limited to the star-topology architecture. We develop Decentralized Federated Domain Generalization with Style Sharing ($\textit{StyleDDG}$), a decentralized DG algorithm which allows devices in a peer-to-peer network to achieve DG based on sharing style information inferred from their datasets. Additionally, we provide the first systematic approach to analyzing style-based DG training in decentralized networks. We cast existing centralized DG algorithms within our framework, and employ their formalisms to model $\textit{StyleDDG}$. We then obtain analytical conditions under which convergence of $\textit{StyleDDG}$ can be guaranteed. Through experiments on popular DG datasets, we demonstrate that $\textit{StyleDDG}$ can obtain significant improvements in accuracy across target domains with minimal communication overhead compared to baseline decentralized gradient methods.