Accelerating Convergence of Replica Exchange Stochastic Gradient MCMC via Variance Reduction
arXiv:2010.01084
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 () 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.
arXiv commentAccepted by ICLR 2021
References in corpus (12)
- On Calibration of Modern Neural Networks
- SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives
- The pseudo-marginal approach for efficient Monte Carlo computations
- Stochastic Gradient Hamiltonian Monte Carlo
- Speeding Up MCMC by Efficient Data Subsampling
- Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks
- On the Convergence of Stochastic Gradient MCMC Algorithms with High-Order Integrators
- Cyclical Stochastic Gradient MCMC for Bayesian Deep Learning
- Stop Wasting My Gradients: Practical SVRG
- Mimicking the marginal distributions of a semimartingale
- Non-convex Learning via Replica Exchange Stochastic Gradient MCMC
- Accelerating Nonconvex Learning via Replica Exchange Langevin Diffusion