Gradient-free Riemannian Langevin Sampler

2026-07-09 · Source: cs.LG updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

The Gradient-free Riemannian Langevin Sampler (GRiLS) is a novel Markov Chain Monte Carlo (MCMC) method designed for efficiently sampling multimodal probability distributions, which often challenge standard MCMC with poor mixing. GRiLS improves exploration by introducing a Riemannian metric that reshapes local geometry, facilitating transitions between modes, crucially without requiring gradient evaluations of the target density. This makes it ideal for complex, computationally expensive targets lacking derivatives. The method estimates the target density's mean and covariance using an ensemble of interacting particles. Its block-ensemble variant, BE-GRiLS, demonstrated superior mixing and mode coverage on 2D benchmarks (e.g., two moons, two rings) and achieved the lowest mean and covariance errors on a 10-dimensional Gaussian mixture, outperforming adaptive Metropolis, MALA, and AIES.

Key takeaway

For AI Scientists and Research Scientists developing or applying MCMC methods to complex, high-dimensional, or multimodal distributions, Gradient-free Riemannian Langevin Sampler (GRiLS) presents a robust solution. Its ability to operate without gradient information, coupled with the enhanced mixing of its Block-Ensemble variant (BE-GRiLS), offers superior accuracy and mode coverage. You should consider integrating BE-GRiLS into your sampling toolkit to overcome mode trapping and improve convergence for challenging targets, while carefully tuning the step size.

Key insights

GRiLS enhances multimodal MCMC exploration by using a gradient-free Riemannian metric to reshape local geometry.

Principles

• Riemannian metrics improve MCMC mixing by reshaping local geometry.
• Gradient-free MCMC is effective for targets lacking derivatives.
• Ensemble methods can estimate target density parameters for MCMC.

Method

GRiLS discretizes a preconditioned Langevin dynamic via a Lamperti transform, estimating target mean and covariance from an ensemble of particles, updated in parallel blocks.

In practice

• Employ GRiLS for sampling distributions with intractable or costly gradients.
• Utilize BE-GRiLS with block updates for parallelized, efficient particle sampling.
• Consider GRiLS for multimodal targets prone to mode trapping with standard MCMC.

Topics

• Gradient-free MCMC
• Riemannian Langevin Dynamics
• Multimodal Sampling
• Ensemble Methods
• Markov Chain Monte Carlo
• Computational Statistics

Code references

• baptistar/GradientFreeRiemannianLangevinSampler

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.LG updates on arXiv.org.