Stein Boltzmann Sampling: A Variational Approach for Global Optimization

Gaëtan Serré, Argyris Kalogeratos, Nicolas Vayatis
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:757-765, 2025.

Abstract

In this paper, we present a deterministic particle-based method for global optimization of continuous Sobolev functions, called \emph{Stein Boltzmann Sampling} (SBS). SBS initializes uniformly a number of particles representing candidate solutions, then uses the \emph{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 $\mathbb{R}^d$, 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-serre25a, title = {Stein Boltzmann Sampling: A Variational Approach for Global Optimization}, author = {Serr{\'e}, Ga{\"e}tan and Kalogeratos, Argyris and Vayatis, Nicolas}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {757--765}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/serre25a/serre25a.pdf}, url = {https://proceedings.mlr.press/v258/serre25a.html}, abstract = {In this paper, we present a deterministic particle-based method for global optimization of continuous Sobolev functions, called \emph{Stein Boltzmann Sampling} (SBS). SBS initializes uniformly a number of particles representing candidate solutions, then uses the \emph{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 $\mathbb{R}^d$, 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.} }
Endnote
%0 Conference Paper %T Stein Boltzmann Sampling: A Variational Approach for Global Optimization %A Gaëtan Serré %A Argyris Kalogeratos %A Nicolas Vayatis %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-serre25a %I PMLR %P 757--765 %U https://proceedings.mlr.press/v258/serre25a.html %V 258 %X In this paper, we present a deterministic particle-based method for global optimization of continuous Sobolev functions, called \emph{Stein Boltzmann Sampling} (SBS). SBS initializes uniformly a number of particles representing candidate solutions, then uses the \emph{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 $\mathbb{R}^d$, 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.
APA
Serré, G., Kalogeratos, A. & Vayatis, N.. (2025). Stein Boltzmann Sampling: A Variational Approach for Global Optimization. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:757-765 Available from https://proceedings.mlr.press/v258/serre25a.html.

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