# Accelerating Convergence of Replica Exchange Stochastic Gradient MCMC via Variance Reduction

arXiv: https://arxiv.org/abs/2010.01084 · HTML: https://mlsanity.com/paper/2010.01084/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2020.

## Built on by (most cited first, 10 of 10)

- [On Convergence of Federated Averaging Langevin Dynamics](https://mlsanity.com/paper/2112.05120/) (2021)
- [Interacting Contour Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2202.09867/) (2022)
- [Non-reversible Parallel Tempering for Deep Posterior Approximation](https://mlsanity.com/paper/2211.10837/) (2022)
- [Balance is Essence: Accelerating Sparse Training via Adaptive Gradient Correction](https://mlsanity.com/paper/2301.03573/) (2023)
- [Active Learning with Bayesian Multi-Fidelity Laplace Neural Operators for Oscillatory Parametric PDEs](https://mlsanity.com/paper/2502.00550/) (2025)
- [EGG-SR: Embedding Symbolic Equivalence into Symbolic Regression via Equality Graph](https://mlsanity.com/paper/2511.05849/) (2025)
- [Enhancing Gradient-based Discrete Sampling via Parallel Tempering](https://mlsanity.com/paper/2502.19240/) (2025)
- [Exploring Non-Convex Discrete Energy Landscapes: An Efficient Langevin-Like Sampler with Replica Exchange](https://mlsanity.com/paper/2501.17323/) (2025)
- [Jeffreys Flow: Robust Boltzmann Generators for Rare Event Sampling via Parallel Tempering Distillation](https://mlsanity.com/paper/2604.05303/) (2026)
- [Mode Coverage in Normalizing Flow Boltzmann Generators via Log-Ratio Variation](https://mlsanity.com/paper/2609.09473/) (2026)

## Abstract (arXiv)

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 Gr"owall'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.