On stochastic gradient Langevin dynamics with dependent data streams: the fully non-convex case
This addresses a theoretical limitation in stochastic optimization for non-convex settings, but it is incremental as it builds on prior work by improving convergence bounds.
The paper tackles the problem of sampling from non-logconcave target distributions using Stochastic Gradient Langevin Dynamics (SGLD) with dependent data streams, establishing sharper and uniform non-asymptotic convergence estimates in the L1-Wasserstein distance.
We consider the problem of sampling from a target distribution, which is \emph {not necessarily logconcave}, in the context of empirical risk minimization and stochastic optimization as presented in Raginsky et al. (2017). Non-asymptotic analysis results are established in the $L^1$-Wasserstein distance for the behaviour of Stochastic Gradient Langevin Dynamics (SGLD) algorithms. We allow the estimation of gradients to be performed even in the presence of \emph{dependent} data streams. Our convergence estimates are sharper and \emph{uniform} in the number of iterations, in contrast to those in previous studies.