DIGing--SGLD: Decentralized and Scalable Langevin Sampling over Time--Varying Networks

Abstract:Sampling from a target distribution induced by training data is central to Bayesian learning, with Stochastic Gradient Langevin Dynamics (SGLD) serving as a key tool for scalable posterior sampling and decentralized variants enabling learning when data are distributed across a network of agents. This paper introduces DIGing-SGLD, a decentralized SGLD algorithm designed for scalable Bayesian learning in multi-agent systems operating over time-varying networks. Existing decentralized SGLD methods are restricted to static network topologies, and many exhibit steady-state sampling bias caused by network effects, even when full batches are used. DIGing-SGLD overcomes these limitations by integrating Langevin-based sampling with the gradient-tracking mechanism of the DIGing algorithm, originally developed for decentralized optimization over time-varying networks, thereby enabling efficient and bias-free sampling without a central coordinator. To our knowledge, we provide the first finite-time non-asymptotic Wasserstein convergence guarantees for decentralized SGLD-based sampling over time-varying networks, with explicit constants. Under standard strong convexity and smoothness assumptions, DIGing-SGLD achieves geometric convergence to an $O(\sqrt{\eta})$ neighborhood of the target distribution, where $\eta$ is the stepsize, with dependence on the target accuracy matching the best-known rates for centralized and static-network SGLD algorithms using constant stepsize. Numerical experiments on Bayesian linear and logistic regression validate the theoretical results and demonstrate the strong empirical performance of DIGing-SGLD under dynamically evolving network conditions.

Optimization and Control (math.OC); Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2511.12836 [math.OC]

(or arXiv:2511.12836v2 [math.OC] for this version)

https://doi.org/10.48550/arXiv.2511.12836 Focus to learn more arXiv-issued DOI via DataCite

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