Accelerating Convergence of Replica Exchange Stochastic Gradient MCMC via Variance Reduction

Deng, W; Feng, Q; Karagiannis, G; Lin, G; Liang, F

Abstract

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

Citation

Deng, W., Feng, Q., Karagiannis, G., Lin, G., & Liang, F. (2021, December). Accelerating Convergence of Replica Exchange Stochastic Gradient MCMC via Variance Reduction. Paper presented at International Conference on Learning Representations (ICLR'21), Virtual Event

• Presentation Conference Type: Conference Paper (unpublished)
• Conference Name: International Conference on Learning Representations (ICLR'21)
• Deposit Date: Feb 10, 2021
• Public URL: https://durham-repository.worktribe.com/output/1139804
• Publisher URL: https://iclr.cc/
• Related Public URLs: https://doi.org/10.48550/arXiv.2010.01084