Stein Boltzmann Sampling: A Variational Approach for Global Optimization

• URL: http://arxiv.org/abs/2402.04689v6
• Date: Thu, 20 Feb 2025 10:08:51 GMT
• Title: Stein Boltzmann Sampling: A Variational Approach for Global Optimization
• Authors: Gaëtan Serré, Argyris Kalogeratos, Nicolas Vayatis,
• Abstract summary: We present a flow-based method for global optimization of continuous Sobolev functions, called Stein Boltzmann Sampling (SBS)<n>A detailed comparison with state-of-the-art methods on benchmark functions demonstrates that SBS and its variants are highly competitive.
• Score: 6.584366906288068
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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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