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On the Theory of Variance Reduction for Stochastic Gradient Monte Carlo
Niladri Chatterji · Nicolas Flammarion · Yian Ma · Peter Bartlett · Michael Jordan

Fri Jul 13 07:50 AM -- 08:00 AM (PDT) @ A4

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.

Author Information

Niladri Chatterji (UC Berkeley)
Nicolas Flammarion (UC Berkeley)
Yian Ma (UC Berkeley)
Peter Bartlett (UC Berkeley)
Michael Jordan (UC Berkeley)

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