ICML 2025

Understanding the Statistical Accuracy-Communication Trade-off in
Personalized Federated Learning with Minimax Guarantees
Xin Yu * 1 Zelin He * 1 Ying Sun 2 Lingzhou Xue 1 Runze Li 1
Abstract
Personalized federated learning (PFL) offers a
flexible framework for aggregating information
across distributed clients with heterogeneous data.
This work considers a personalized federated
learning setting that simultaneously learns global
and local models. While purely local training
has no communication cost, collaborative learn-
ing among the clients can leverage shared knowl-
edge to improve statistical accuracy, presenting
an accuracy-communication trade-off in personal-
ized federated learning. However, the theoretical
analysis of how personalization quantitatively in-
fluences sample and algorithmic efficiency and
their inherent trade-off is largely unexplored. This
paper makes a contribution towards filling this
gap, by providing a quantitative characterization
of the personalization degree on the tradeoff. The
results further offers theoretical insights for choos-
ing the personalization degree. As a side contri-
bution, we establish the minimax optimality in
terms of statistical accuracy for a widely studied
PFL formulation. The theoretical result is vali-
dated on both synthetic and real-world datasets
and its generalizability is verified in a non-convex
setting.
1. Introduction
Federated Learning (FL) (McMahan et al., 2017) has
emerged as a promising learning framework for aggregating
information from distributed data, allowing clients to collab-
oratively train a shared global model in a communication-
efficient manner. However, a critical challenge arising in
*Equal contribution
1Department of Statistics, The Pennsyl-
vania State University, University Park, PA 16802, USA 2School
of Electrical Engineering and Computer Science, The Pennsyl-
vania State University, University Park, PA 16802, USA. Corre-
spondence to: Ying Sun <ybs5190@psu.edu>, Lingzhou Xue
<lzxue...