Subsampled Stochastic Variance-Reduced Gradient Langevin Dynamics

Difan Zou, Pan Xu, Quanquan Gu
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:507-517, 2018.

Abstract

Stochastic variance-reduced gradient Langevin dynamics (SVRG-LD) was recently proposed to improve the performance of stochastic gra- dient Langevin dynamics (SGLD) by reduc- ing the variance of the stochastic gradient. In this paper, we propose a variant of SVRG-LD, namely SVRG-LD+, which replaces the full gradient in each epoch with a subsampled one. We provide a nonasymptotic analysis of the convergence of SVRG-LD+ in 2-Wasserstein distance, and show that SVRG-LD+ enjoys a lower gradient complexity1 than SVRG-LD, when the sample size is large or the target ac- curacy requirement is moderate. Our analysis directly implies a sharper convergence rate for SVRG-LD, which improves the existing con- vergence rate by a factor of $\kappa$1/6n1/6, where $\kappa$ is the condition number of the log-density function and n is the sample size. Experiments on both synthetic and real-world datasets vali- date our theoretical results.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-zou18a, title = {Subsampled Stochastic Variance-Reduced Gradient {L}angevin Dynamics}, author = {Zou, Difan and Xu, Pan and Gu, Quanquan}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {507--517}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/zou18a/zou18a.pdf}, url = {https://proceedings.mlr.press/r16/zou18a.html}, abstract = {Stochastic variance-reduced gradient Langevin dynamics (SVRG-LD) was recently proposed to improve the performance of stochastic gra- dient Langevin dynamics (SGLD) by reduc- ing the variance of the stochastic gradient. In this paper, we propose a variant of SVRG-LD, namely SVRG-LD+, which replaces the full gradient in each epoch with a subsampled one. We provide a nonasymptotic analysis of the convergence of SVRG-LD+ in 2-Wasserstein distance, and show that SVRG-LD+ enjoys a lower gradient complexity1 than SVRG-LD, when the sample size is large or the target ac- curacy requirement is moderate. Our analysis directly implies a sharper convergence rate for SVRG-LD, which improves the existing con- vergence rate by a factor of $\kappa$1/6n1/6, where $\kappa$ is the condition number of the log-density function and n is the sample size. Experiments on both synthetic and real-world datasets vali- date our theoretical results.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Subsampled Stochastic Variance-Reduced Gradient Langevin Dynamics %A Difan Zou %A Pan Xu %A Quanquan Gu %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-zou18a %I PMLR %P 507--517 %U https://proceedings.mlr.press/r16/zou18a.html %V R16 %X Stochastic variance-reduced gradient Langevin dynamics (SVRG-LD) was recently proposed to improve the performance of stochastic gra- dient Langevin dynamics (SGLD) by reduc- ing the variance of the stochastic gradient. In this paper, we propose a variant of SVRG-LD, namely SVRG-LD+, which replaces the full gradient in each epoch with a subsampled one. We provide a nonasymptotic analysis of the convergence of SVRG-LD+ in 2-Wasserstein distance, and show that SVRG-LD+ enjoys a lower gradient complexity1 than SVRG-LD, when the sample size is large or the target ac- curacy requirement is moderate. Our analysis directly implies a sharper convergence rate for SVRG-LD, which improves the existing con- vergence rate by a factor of $\kappa$1/6n1/6, where $\kappa$ is the condition number of the log-density function and n is the sample size. Experiments on both synthetic and real-world datasets vali- date our theoretical results. %Z Reissued by PMLR on 04 October 2026.
APA
Zou, D., Xu, P. & Gu, Q.. (2018). Subsampled Stochastic Variance-Reduced Gradient Langevin Dynamics. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:507-517 Available from https://proceedings.mlr.press/r16/zou18a.html. Reissued by PMLR on 04 October 2026.

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