Accelerating Convergence of Replica Exchange Stochastic Gradient MCMC\n via Variance Reduction

2020/10/02 by Wei Deng, Deng, Wei, Qi Feng +7 · 2 citations
Mathematics · Computer Science · Medicine · #Markov Chains and Monte Carlo Methods #Stochastic Gradient Optimization Techniques #Advanced Neuroimaging Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2010.01084

Abstract

Replica exchange stochastic gradient Langevin dynamics (reSGLD) has shown\npromise in accelerating the convergence in non-convex learning; however, an\nexcessively large correction for avoiding biases from noisy energy estimators\nhas limited the potential of the acceleration. To address this issue, we study\nthe variance reduction for noisy energy estimators, which promotes much more\neffective swaps. Theoretically, we provide a non-asymptotic analysis on the\nexponential acceleration for the underlying continuous-time Markov jump\nprocess; moreover, we consider a generalized Girsanov theorem which includes\nthe change of Poisson measure to overcome the crude discretization based on the\nGr "owall's inequality and yields a much tighter error in the 2-Wasserstein\n(\W₂) distance. Numerically, we conduct extensive experiments and\nobtain the state-of-the-art results in optimization and uncertainty estimates\nfor synthetic experiments and image data.\n

Citations

• A Stochastic Approximation Method
• The pseudo-marginal approach for efficient Monte Carlo computations

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