Sampling from Non-Log-Concave Distributions via Stochastic Variance-Reduced Gradient Langevin Dynamics

We study stochastic variance reduction-based Langevin dynamic algorithms, SVRG-LD and SAGA-LD (Dubey et al., 2016), for sampling from non-log-concave distributions. Under certain assumptions on the log density function, we establish the convergence guarantees of SVRG-LD and SAGA-LD in 2-Wasserstein distance. More specifically, we show that both SVRG-LD and SAGA-LD require (Formula present) stochastic gradient evaluations to achieve e-accuracy in 2-Wasserstein distance, which outperforms the (Formula present) gradient complexity achieved by Langevin Monte Carlo Method (Raginsky et al., 2017). Experiments on synthetic data and real data back up our theory.

Duke Scholars

Author Pan Xu Biostatistics & Bioinformatics, Division of Translational Bi ...