New non-reversible Langevin technique cuts Bayesian sampling variance

A new arXiv paper from Ni, Wang, Wang, and Zhu tackles a fundamental challenge in Bayesian machine learning: how to efficiently sample from high-dimensional posterior distributions using stochastic gradients. The authors study variance reduction for generalized non-reversible Langevin Monte Carlo algorithms, a class of sampling methods that break detailed balance to accelerate mixing. Their theoretical contribution proves a central limit theorem (CLT) for the empirical average under a small-stepsize regime, characterizing the limiting variance via the Poisson equation of the full-gradient diffusion. They derive a sufficient condition showing that adding an anti-symmetric perturbation strictly reduces this asymptotic variance compared to reversible Langevin dynamics, providing a rigorous foundation for faster sampling.

To validate their theory, the team tested the method on Bayesian linear regression with synthetic data and Bayesian logistic regression on real-world datasets. The numerical experiments confirm that non-reversible schemes consistently reduce root mean squared error (RMSE) relative to reversible baselines, matching the predicted Gaussian fluctuations. The framework also covers augmented-state models like Hessian-free high-resolution dynamics and gradient-adjusted underdamped Langevin dynamics. This work bridges theoretical guarantees with practical gains, offering ML practitioners a principled way to speed up Markov chain Monte Carlo without sacrificing accuracy.