Client-specific or hierarchical deviation scales

Develop a more flexible deviation-scale model that replaces the globally shared scale with client-specific scales or a hierarchical prior over the collection of client-specific scales, while preserving tractable federated optimization and controlling communication and server-side hyperparameter complexity.

Background

The pFedHGP model parameterizes the deviation kernel as kδ=ϕkgk_\delta=\phi k_g, where ϕ>0\phi>0 is a single globally shared hyperparameter controlling the prior variance of systematic client deviations. Although each client has its own variational posterior for the deviation process, all clients share the same prior scale.

The paper notes that allowing client-specific scales or a hierarchical prior could represent heterogeneous deviation magnitudes more flexibly. This extension is not developed because it would increase communication and server-side hyperparameter complexity.

References

A more flexible extension would replace the shared \phi with client-specific scales \phi_i or a hierarchical prior over {\phi_i}; we leave this extension for future work to avoid increasing communication and server-side hyperparameter complexity.

— Personalized Federated Hierarchical Gaussian Processes for Privacy-Preserving Modeling of Heterogeneous Distributed Systems  (2609.19337 - Xie et al., 16 Sep 2026) in Section 2.3, paragraph "Deviation scale \(\phi\) as a federated hyperparameter"