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

2025-11-16

AI Summary

Existing decentralized stochastic gradient Langevin dynamics (SGLD) methods assume static network topologies and suffer from network-induced stationary sampling bias, even under full-batch settings. This limits their applicability to multi-agent Bayesian learning over time-varying communication graphs. Method: We propose DSGLD—the first decentralized Langevin sampling algorithm supporting dynamic topologies—by integrating gradient tracking into the SGLD framework, combining the DIGing structure with stochastic gradient Langevin dynamics, and employing constant step sizes to achieve geometric convergence. Contribution/Results: We provide the first finite-time Wasserstein-2 distance convergence guarantee for decentralized Langevin sampling, establishing that the iterates’ distribution approximates the target posterior within $O(sqrt{eta})$ error, where $eta$ is the step size. Experiments demonstrate that DSGLD significantly outperforms existing distributed sampling methods on time-varying networks, validating both theoretical claims and practical efficacy.

Technology Category

• Machine Learning: Distributed Machine Learning & Federated Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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 $O(sqrtη)$ neighborhood of the target distribution, where $η$ 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.

Problem

• Enables decentralized Bayesian sampling over time-varying network topologies
• Eliminates steady-state sampling bias through gradient-tracking integration
• Provides finite-time convergence guarantees for distributed Langevin dynamics

Innovation

• Decentralized SGLD algorithm for time-varying networks
• Integrates Langevin sampling with DIGing gradient tracking
• Provides finite-time convergence guarantees for bias-free sampling