# Stein Boltzmann Sampling: A Variational Approach for Global Optimization

arXiv: https://arxiv.org/abs/2402.04689 · HTML: https://mlsanity.com/paper/2402.04689/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 18 of 18)

- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Non-convex learning via Stochastic Gradient Langevin Dynamics: a nonasymptotic analysis](https://mlsanity.com/paper/1702.03849/) (2017)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [Stein Variational Gradient Descent as Gradient Flow](https://mlsanity.com/paper/1704.07520/) (2017)
- [The Lean mathematical library](https://mlsanity.com/paper/1910.09336/) (2019)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [On the geometry of Stein variational gradient descent](https://mlsanity.com/paper/1912.00894/) (2019)
- [A Non-Asymptotic Analysis for Stein Variational Gradient Descent](https://mlsanity.com/paper/2006.09797/) (2020)
- [Kernel Stein Discrepancy Descent](https://mlsanity.com/paper/2105.09994/) (2021)
- [Global Non-convex Optimization with Discretized Diffusions](https://mlsanity.com/paper/1810.12361/) (2018)
- [Global optimization of Lipschitz functions](https://mlsanity.com/paper/1703.02628/) (2017)
- [A gradient sampling method with complexity guarantees for Lipschitz functions in high and low dimensions](https://mlsanity.com/paper/2112.06969/) (2021)
- [Scaling limit of the Stein variational gradient descent: the mean field regime](https://mlsanity.com/paper/1805.04035/) (2018)
- [Finding Global Minima via Kernel Approximations](https://mlsanity.com/paper/2012.11978/) (2020)
- [BayesOpt: A Bayesian Optimization Library for Nonlinear Optimization, Experimental Design and Bandits](https://mlsanity.com/paper/1405.7430/) (2014)
- [Convergence of Stein Variational Gradient Descent under a Weaker Smoothness Condition](https://mlsanity.com/paper/2206.00508/) (2022)
- [On quantitative Laplace-type convergence results for some exponential probability measures, with two applications](https://mlsanity.com/paper/2110.12922/) (2021)
- [Minima distribution for global optimization](https://mlsanity.com/paper/1812.03457/) (2018)

## Built on by (most cited first, 2 of 2)

- [Multi-view diffusion geometry using intertwined diffusion trajectories](https://mlsanity.com/paper/2512.01484/) (2025)
- [B3O: Scalable Boltzmann Batch Bayesian Optimization](https://mlsanity.com/paper/2606.30228/) (2026)

## Abstract (arXiv)

In this paper, we present a flow-based method for global optimization of continuous Sobolev functions, called Stein Boltzmann Sampling (SBS). SBS initializes uniformly a number of particles representing candidate solutions, then uses the Stein Variational Gradient Descent (SVGD) algorithm to sequentially and deterministically move those particles in order to approximate a target distribution whose mass is concentrated around promising areas of the domain of the optimized function. The target is chosen to be a properly parametrized Boltzmann distribution. For the purpose of global optimization, we adapt the generic SVGD theoretical framework allowing to address more general target distributions over a compact subset of ℝd, and we prove SBS's asymptotic convergence. In addition to the main SBS algorithm, we present two variants: the SBS-PF that includes a particle filtering strategy, and the SBS-HYBRID one that uses SBS or SBS-PF as a continuation after other particle- or distribution-based optimization methods. A detailed comparison with state-of-the-art methods on benchmark functions demonstrates that SBS and its variants are highly competitive, while the combination of the two variants provides the best trade-off between accuracy and computational cost.