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Qinglun Li

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ICLR Conference 2025 Conference Paper

Understanding the Stability-based Generalization of Personalized Federated Learning

Yingqi Liu
Qinglun Li
Jie Tang 0001
Yifan Shi
Li Shen 0008
Xiaochun Cao

Despite great achievements in algorithm design for Personalized Federated Learning (PFL), research on the theoretical analysis of generalization is still in its early stages. Some theoretical results have investigated the generalization performance of personalized models under the problem setting and hypothesis in convex conditions, which can not reflect the real iteration performance during non-convex training. To further understand the real performance from a generalization perspective, we propose the first algorithm-dependent generalization analysis with uniform stability for the typical PFL method, Partial Model Personalization, on smooth and non-convex objectives. Specifically, we decompose the generalization errors into aggregation errors and fine-tuning errors, then creatively establish a generalization analysis framework corresponding to the gradient estimation process of the personalized training. This framework builds up the bridge among PFL, FL and Pure Local Training for personalized aims in heterogeneous scenarios, which clearly demonstrates the effectiveness of PFL from the generalization perspective. Moreover, we demonstrate the impact of trivial factors like learning steps, stepsizes and communication topologies and obtain the excess risk analysis with optimization errors for PFL. Promising experiments on CIFAR datasets also corroborate our theoretical insights. Our code can be seen in https://github.com/YingqiLiu1999/Understanding-the-Stability-based-Generalization-of-Personalized-Federated-Learning.

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NeurIPS Conference 2025 Conference Paper

Unveiling the Power of Multiple Gossip Steps: A Stability-Based Generalization Analysis in Decentralized Training

Qinglun Li
Yingqi Liu
Miao Zhang
Xiaochun Cao
Quanjun Yin
Li Shen

Decentralized training removes the centralized server, making it a communication-efficient approach that can significantly improve training efficiency, but it often suffers from degraded performance compared to centralized training. Multi-Gossip Steps (MGS) serve as a simple yet effective bridge between decentralized and centralized training, significantly reducing experiment performance gaps. However, the theoretical reasons for its effectiveness and whether this gap can be fully eliminated by MGS remain open questions. In this paper, we derive upper bounds on the generalization error and excess error of MGS using stability analysis, systematically answering these two key questions. 1). Optimization Error Reduction: MGS reduces the optimization error bound at an exponential rate, thereby exponentially tightening the generalization error bound and enabling convergence to better solutions. 2). Gap to Centralization: Even as MGS approaches infinity, a non-negligible gap in generalization error remains compared to centralized mini-batch SGD ($\mathcal{O}(T^{\frac{c\beta}{c\beta +1}}/{n m})$ in centralized and $\mathcal{O}(T^{\frac{2c\beta}{2c\beta +2}}/{n m^{\frac{1}{2c\beta +2}}})$ in decentralized). Furthermore, we provide the first unified analysis of how factors like learning rate, data heterogeneity, node count, per-node sample size, and communication topology impact the generalization of MGS under non-convex settings without the bounded gradients assumption, filling a critical theoretical gap in decentralized training. Finally, promising experiments on CIFAR datasets support our theoretical findings.

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