Robust Stochastic Gradient Posterior Sampling with Lattice Based Discretisation

2026-02-17

AI Summary

This work addresses the instability of stochastic gradient Markov Chain Monte Carlo (SG-MCMC) methods under small-batch sampling and heavy-tailed gradient noise, which can compromise posterior inference. The authors propose SGLRW, a novel SG-MCMC algorithm that, for the first time, incorporates lattice-based random walk discretization into the SG-MCMC framework. By injecting random noise exclusively into the off-diagonal elements of the covariance matrix, SGLRW significantly enhances robustness to both batch size and gradient noise while preserving asymptotic unbiasedness. Empirical evaluations on Bayesian regression and classification tasks demonstrate that SGLRW remains stable in scenarios where stochastic gradient Langevin dynamics (SGLD) fails, achieving predictive performance on par with or superior to existing methods.

Technology Category

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

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Architectures and workflows that use LLMs for crowd work

Abstract

Stochastic-gradient MCMC methods enable scalable Bayesian posterior sampling but often suffer from sensitivity to minibatch size and gradient noise. To address this, we propose Stochastic Gradient Lattice Random Walk (SGLRW), an extension of the Lattice Random Walk discretization. Unlike conventional Stochastic Gradient Langevin Dynamics (SGLD), SGLRW introduces stochastic noise only through the off-diagonal elements of the update covariance; this yields greater robustness to minibatch size while retaining asymptotic correctness. Furthermore, as comparison we analyze a natural analogue of SGLD utilizing gradient clipping. Experimental validation on Bayesian regression and classification demonstrates that SGLRW remains stable in regimes where SGLD fails, including in the presence of heavy-tailed gradient noise, and matches or improves predictive performance.

Problem

• stochastic gradient MCMC
• minibatch sensitivity
• gradient noise
• Bayesian posterior sampling
• robustness

Innovation

• Stochastic Gradient MCMC
• Lattice Random Walk
• Gradient Noise Robustness
• Bayesian Posterior Sampling
• Minibatch Stability