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.

本文研究了针对Wasserstein距离的多种变量减少方法（包括SAGA Langevin扩散、SVRG Langevin扩散和控制变量欠阻尼Langevin扩散）的收敛性保证，同时对后验分布进行了一致的假设：光滑、强凸和Hessian Lipschitz。通过一种新的证明技术，结合了有限和最优化与抽样方法分析的思想，我们得到了尖锐的理论上界，可以确定每种方法比其他方法更好的兴趣范围，并通过对真实世界和合成数据集的实验验证了我们的理论。

随机梯度蒙特卡罗方差减小理论