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

2025-10-09

AI Summary

The theoretical foundations underlying the generalization performance of multi-step gossip (MGS) in decentralized training remain unclear, and it is unknown whether MGS can fully bridge the performance gap with centralized training. Method: This paper proposes the first unified generalization error analysis framework grounded in algorithmic stability, applicable to non-convex settings without requiring bounded gradient assumptions. It systematically characterizes the impacts of learning rate, data heterogeneity, number of nodes, local sample size, and communication topology on both generalization and optimization errors of MGS. Results: We theoretically establish that MGS achieves exponential convergence of optimization error; however, even asymptotically, an inherent generalization gap persists between decentralized and centralized training—determined solely by network topology and data heterogeneity. Empirical validation on CIFAR datasets confirms the tightness and practical guidance of our theoretical bounds.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Search and Optimization: Non-convex Optimization
• Multiagent Systems: Other Foundations of Multi Agent Systems

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

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 ($mathcal{O}(T^{frac{cβ}{cβ+1}}/{n m})$ in centralized and $mathcal{O}(T^{frac{2cβ}{2cβ+2}}/{n m^{frac{1}{2cβ+2}}})$ 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.

Problem

• Analyzes generalization error bounds for Multi-Gossip Steps in decentralized training
• Investigates performance gap elimination between decentralized and centralized training
• Examines impact of learning rate and data heterogeneity on generalization

Innovation

• Multi-Gossip Steps reduce optimization error exponentially
• Generalization gap persists compared to centralized training
• Unified analysis covers learning rate and topology impacts