mlsanityData to 14 Oct 2026

On the Convergence of Stochastic Gradient MCMC Algorithms with High-Order Integrators

arXiv 1610.06665 ↗First posted 21 Oct 2016stat.MLcited by 35

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Abstract (arXiv)

Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and the stochastic gradient thermostat. While finite-time convergence properties of the SGLD with a 1st-order Euler integrator have recently been studied, corresponding theory for general SG-MCMCs has not been explored. In this paper we consider general SG-MCMCs with high-order integrators, and develop theory to analyze finite-time convergence properties and their asymptotic invariant measures. Our theoretical results show faster convergence rates and more accurate invariant measures for SG-MCMCs with higher-order integrators. For example, with the proposed efficient 2nd-order symmetric splitting integrator, the em mean square error (MSE) of the posterior average for the SGHMC achieves an optimal convergence rate of L-4/5 at L iterations, compared to L-2/3 for the SGHMC and SGLD with 1st-order Euler integrators. Furthermore, convergence results of decreasing-step-size SG-MCMCs are also developed, with the same convergence rates as their fixed-step-size counterparts for a specific decreasing sequence. Experiments on both synthetic and real datasets verify our theory, and show advantages of the proposed method in two large-scale real applications.

Key facts. Cited by 35 papers in the map (data through 14 Oct 2026). First posted on arXiv 21 Oct 2016.

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Citing papers per year: 2021: 7; 2022: 3; 2023: 9; 2024: 5; 2025: 10; 2026: 1.

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