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Replica exchange enhanced adaptively weighted stochastic gradient Langevin dynamics for Bayesian sampling and

Zhenqing Wu1,2, Wenwu Gong1,2, Ziying Yu1

  • 1Department of Statistics and Data Science, Southern University of Science and Technology, Shenzhen, 518055, China.

Scientific Reports
|May 15, 2025
PubMed
Summary

We introduce the replica exchange adaptively weighted stochastic gradient Langevin dynamics (REAWSGLD) algorithm to improve Bayesian learning. This method enhances Monte Carlo simulation and non-convex optimization in big data by escaping local traps.

Keywords:
1/k-Ensemble samplingMonte Carlo simulationNon-convex optimizationReplica exchangeStochastic gradient Langevin dynamics

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Area of Science:

  • Computational Statistics
  • Machine Learning

Background:

  • Bayesian learning often involves complex energy landscapes.
  • Traditional methods struggle with local traps in non-convex optimization.

Purpose of the Study:

  • To develop an algorithm for effective Bayesian learning in complex energy landscapes.
  • To enhance Monte Carlo simulation and non-convex optimization for big data problems.

Main Methods:

  • Proposing the replica exchange adaptively weighted stochastic gradient Langevin dynamics (REAWSGLD) algorithm.
  • Merging 1/k-ensemble and replica exchange methods with two Langevin dynamics processes at different temperatures.
  • Utilizing lower temperature for local exploitation and higher temperature for global exploration.

Main Results:

  • The REAWSGLD algorithm effectively escapes local traps in simulations.
  • Empirical evaluations demonstrate efficacy in navigating complex energy landscapes.
  • Numerical results show potential for contemporary machine learning tasks.

Conclusions:

  • The REAWSGLD algorithm offers a robust solution for Bayesian learning challenges.
  • The synergistic combination of methods enhances both local exploitation and global exploration.
  • This approach is promising for advanced Monte Carlo simulation and non-convex optimization.