  We provide a new convergence analysis of stochastic gradient Langevin
dynamics (SGLD) for sampling from a class of distributions that can be
non-log-concave. At the core of our approach is a novel conductance analysis of
SGLD using an auxiliary time-reversible Markov Chain. Under certain conditions
on the target distribution, we prove that $\tilde O(d^4\epsilon^{-2})$
stochastic gradient evaluations suffice to guarantee $\epsilon$-sampling error
in terms of the total variation distance, where $d$ is the problem dimension.
This improves existing results on the convergence rate of SGLD (Raginsky et
al., 2017; Xu et al., 2018). We further show that provided an additional
Hessian Lipschitz condition on the log-density function, SGLD is guaranteed to
achieve $\epsilon$-sampling error within $\tilde O(d^{15/4}\epsilon^{-3/2})$
stochastic gradient evaluations. Our proof technique provides a new way to
study the convergence of Langevin-based algorithms and sheds some light on the
design of fast stochastic gradient-based sampling algorithms.
