Stability and Generalization for Decentralized Markov SGD

2026-05-02

AI Summary

This work addresses the lack of generalization theory for stochastic gradient methods under Markov sampling in decentralized settings. It proposes an analysis framework grounded in algorithmic stability, integrating Markov chain mixing theory, graph-based network communication models, and primal-dual optimization dynamics. For the first time, the framework extends generalization analysis under Markov-dependent data to both decentralized SGD and SGDA, unifying the characterization of how network topology and data dependence jointly influence generalization performance. The derived non-asymptotic upper bounds on generalization error reveal a theoretical connection between algorithmic convergence and generalization capability, thereby providing rigorous theoretical support for decentralized minimax learning.

Abstract

Stochastic gradient methods are central to large-scale learning, yet their generalization theory typically relies on independent sampling assumptions. In many practical applications, data are generated by Markov chains and learning is performed in a decentralized manner, which introduces significant analytical challenges. In this work, we investigate the stability and generalization of decentralized stochastic gradient descent (SGD) and stochastic gradient descent ascent (SGDA) under Markov chain sampling. Leveraging a stability-based framework, we characterize how Markovian dependence and decentralized communication jointly influence generalization behavior. Our analysis captures the effects of network topology, Markov chain mixing properties, and primal-dual dynamics. We establish non-asymptotic generalization bounds for both algorithms, extending existing results on Markov stochastic gradient methods to decentralized and minimax settings.

Problem

• Decentralized Learning
• Markov Chain Sampling
• Generalization
• Stochastic Gradient Descent
• Minimax Optimization

Innovation

• Decentralized SGD
• Markov chain sampling
• Generalization bounds
• Stability analysis
• Minimax optimization