# Accelerating Nonconvex Learning via Replica Exchange Langevin Diffusion

arXiv: https://arxiv.org/abs/2007.01990 · HTML: https://mlsanity.com/paper/2007.01990/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jul 2020.

## Built on by (most cited first, 16 of 16)

- [Accelerated replica exchange stochastic gradient Langevin diffusion enhanced Bayesian DeepONet for solving noisy parametric PDEs](https://mlsanity.com/paper/2111.02484/) (2021)
- [Accelerating Approximate Thompson Sampling with Underdamped Langevin Monte Carlo](https://mlsanity.com/paper/2401.11665/) (2024)
- [Provable Convergence and Limitations of Geometric Tempering for Langevin Dynamics](https://mlsanity.com/paper/2410.09697/) (2024)
- [Non-reversible Parallel Tempering for Deep Posterior Approximation](https://mlsanity.com/paper/2211.10837/) (2022)
- [Constrained Exploration via Reflected Replica Exchange Stochastic Gradient Langevin Dynamics](https://mlsanity.com/paper/2405.07839/) (2024)
- [Persistently Trained, Diffusion-assisted Energy-based Models](https://mlsanity.com/paper/2304.10707/) (2023)
- [Accelerating Langevin Monte Carlo Sampling: A Large Deviations Analysis](https://mlsanity.com/paper/2503.19066/) (2025)
- [Anchored Langevin Algorithms](https://mlsanity.com/paper/2509.19455/) (2025)
- [Subsampling Error in Stochastic Gradient Langevin Diffusions](https://mlsanity.com/paper/2305.13882/) (2023)
- [Enhancing Gradient-based Discrete Sampling via Parallel Tempering](https://mlsanity.com/paper/2502.19240/) (2025)
- [Operator-Level Quantum Acceleration of Non-Logconcave Sampling](https://mlsanity.com/paper/2505.05301/) (2025)
- [A New Framework for Variance-Reduced Hamiltonian Monte Carlo](https://mlsanity.com/paper/2102.04613/) (2021)
- [Exploring Non-Convex Discrete Energy Landscapes: An Efficient Langevin-Like Sampler with Replica Exchange](https://mlsanity.com/paper/2501.17323/) (2025)
- [A hierarchical resource-efficient deep policy gradient method for continuous-time optimal control problems](https://mlsanity.com/paper/2502.14141/) (2025)
- [BLADE: Bayesian Langevin Active Discovery with Replica Exchange for Identification of Complex Systems](https://mlsanity.com/paper/2503.02983/) (2025)
- [Mode Coverage in Normalizing Flow Boltzmann Generators via Log-Ratio Variation](https://mlsanity.com/paper/2609.09473/) (2026)

## Abstract (arXiv)

Langevin diffusion is a powerful method for nonconvex optimization, which enables the escape from local minima by injecting noise into the gradient. In particular, the temperature parameter controlling the noise level gives rise to a tradeoff between ``global exploration'' and ``local exploitation'', which correspond to high and low temperatures. To attain the advantages of both regimes, we propose to use replica exchange, which swaps between two Langevin diffusions with different temperatures. We theoretically analyze the acceleration effect of replica exchange from two perspectives: (i) the convergence in chi2-divergence, and (ii) the large deviation principle. Such an acceleration effect allows us to faster approach the global minima. Furthermore, by discretizing the replica exchange Langevin diffusion, we obtain a discrete-time algorithm. For such an algorithm, we quantify its discretization error in theory and demonstrate its acceleration effect in practice.