Pré-Publication, Document De Travail Année : 2025

Stein Boltzmann Sampling: A Variational Approach for Global Optimization

Gaëtan Serré
Argyris Kalogeratos
Nicolas Vayatis

Résumé

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 $\mathbb{R}^d$, 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.
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Dates et versions

hal-04442217 , version 1 (06-02-2024)
hal-04442217 , version 2 (15-02-2024)
hal-04442217 , version 3 (27-02-2024)
hal-04442217 , version 4 (11-03-2024)
hal-04442217 , version 5 (03-05-2024)
hal-04442217 , version 6 (31-05-2024)
hal-04442217 , version 7 (17-02-2025)

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Gaëtan Serré, Argyris Kalogeratos, Nicolas Vayatis. Stein Boltzmann Sampling: A Variational Approach for Global Optimization. 2025. ⟨hal-04442217v7⟩
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