A Convergence Analysis for A Class of Practical Variance-Reduction Stochastic Gradient MCMC

Understand

Stochastic gradient Markov Chain Monte Carlo (SG-MCMC) has been developed as a flexible family of scalable Bayesian sampling algorithms.

• However, there has been little theoretical analysis of the impact of minibatch size to the algorithm's convergence rate.
• In this paper, we prove that under a limited computational budget/time, a larger minibatch size leads to a faster decrease of the mean squared error bound (thus the fastest one corresponds to using full gradients), which motivates the necessity of variance reduction in SG-MCMC.
• Consequently, by borrowing ideas from stochastic optimization, we propose a practical variance-reduction technique for SG-MCMC, that is efficient in both computation and storage.