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Replica exchange stochastic gradient Langevin dynamics (reSGLD) has shownpromise in accelerating the convergence in non-convex learning; however, anexcessively large correction for avoiding biases from noisy energy estimatorshas limited the potential of the acceleration. To address this issue, we studythe variance reduction for noisy energy estimators, which promotes much moreeffective swaps. Theoretically, we provide a non-asymptotic analysis on theexponential acceleration for the underlying continuous-time Markov jumpprocess; moreover, we consider a generalized Girsanov theorem which includesthe change of Poisson measure to overcome the crude discretization based on theGr\"{o}wall's inequality and yields a much tighter error in the 2-Wasserstein($\mathcal{W}_2$) distance. Numerically, we conduct extensive experiments andobtain the state-of-the-art results in optimization and uncertainty estimatesfor synthetic experiments and image data.

Accelerating Convergence of Replica Exchange Stochastic Gradient MCMC via Variance Reduction