On the Theory of Variance Reduction for Stochastic Gradient Monte Carlo
Niladri Chatterji, Nicolas Flammarion, Yian Ma, Peter Bartlett, Michael Jordan
Abstract
We provide convergence guarantees in Wasserstein distance for a variety of variance-reduction methods: SAGA Langevin diffusion, SVRG Langevin diffusion and control-variate underdamped Langevin diffusion. We analyze these methods under a uniform set of assumptions on the log-posterior distribution, assuming it to be smooth, strongly convex and Hessian Lipschitz. This is achieved by a new proof technique combining ideas from finite-sum optimization and the analysis of sampling methods. Our sharp theoretical bounds allow us to identify regimes of interest where each method performs better than the others. Our theory is verified with experiments on real-world and synthetic datasets.
BibTeX
@InProceedings{pmlr-v80-chatterji18a,
title = {On the Theory of Variance Reduction for Stochastic Gradient {M}onte {C}arlo},
author = {Chatterji, Niladri and Flammarion, Nicolas and Ma, Yian and Bartlett, Peter and Jordan, Michael},
booktitle = {Proceedings of the 35th International Conference on Machine Learning},
pages = {764--773},
year = {2018},
editor = {Dy, Jennifer and Krause, Andreas},
volume = {80},
series = {Proceedings of Machine Learning Research},
month = {10--15 Jul},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v80/chatterji18a/chatterji18a.pdf},
url = {https://proceedings.mlr.press/v80/chatterji18a.html},
abstract = {We provide convergence guarantees in Wasserstein distance for a variety of variance-reduction methods: SAGA Langevin diffusion, SVRG Langevin diffusion and control-variate underdamped Langevin diffusion. We analyze these methods under a uniform set of assumptions on the log-posterior distribution, assuming it to be smooth, strongly convex and Hessian Lipschitz. This is achieved by a new proof technique combining ideas from finite-sum optimization and the analysis of sampling methods. Our sharp theoretical bounds allow us to identify regimes of interest where each method performs better than the others. Our theory is verified with experiments on real-world and synthetic datasets.}
}