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 2Wasserstein distance. More specifically, we show that both SVRG-LD and SAGA-LD require Õ ( n+n/ +n/ 4 ) ·exp ( Õ(d+γ) ) stochastic gradient evaluations to achieve accuracy in 2-Wasserstein distance, which outperforms the Õ ( n/ 4 ) · exp ( Õ(d + γ) ) gradient complexity achieved by Langevin Monte Carlo Method (Raginsky et al., 2017). Experiments on synthetic data and real data back up our theory.

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