In this paper, we introduce a new flow-based method for global optimization of Lipschitz functions, called Stein Boltzmann Sampling (SBS). Our method samples from the Boltzmann distribution that becomes asymptotically uniform over the set of the minimizers of the function to be optimized. Candidate solutions are sampled via the \emph{Stein Variational Gradient Descent} algorithm. We prove the asymptotic convergence of our method, introduce two SBS variants, and provide a detailed comparison with several state-of-the-art global optimization algorithms on various benchmark functions. The design of our method, the theoretical results, and our experiments, suggest that SBS is particularly well-suited to be used as a continuation of efficient global optimization methods as it can produce better solutions while making a good use of the budget.

翻译：本文提出了一种新的基于流的Lipschitz函数全局优化方法，称为斯坦因玻尔兹曼采样（Stein Boltzmann Sampling, SBS）。该方法从玻尔兹曼分布中采样，该分布渐近均匀分布于待优化函数最小值点集上。候选解通过*斯坦因变分梯度下降*（Stein Variational Gradient Descent）算法进行采样。我们证明了该方法的渐近收敛性，提出了两种SBS变体，并在多种基准函数上与若干先进全局优化算法进行了详细比较。该方法的设计、理论结果及实验表明，SBS特别适合作为高效全局优化方法的延续，因为它能在充分利用预算的同时产生更优解。