Stability and Generalization for Decentralized Markov SGD

TL;DR

This paper analyzes how decentralized Markov chain sampling affects the stability and generalization of stochastic gradient methods, providing new theoretical bounds in complex networked learning scenarios.

Contribution

It introduces a stability-based framework to characterize the impact of Markov dependence and decentralization on generalization in SGD and SGDA.

Findings

Established non-asymptotic generalization bounds for decentralized Markov SGD and SGDA.

Extended existing Markov stochastic gradient results to decentralized and minimax settings.

Analyzed effects of network topology and Markov chain mixing on learning stability.

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.