Stein Boltzmann Sampling: A Variational Approach for Global Optimization
arxiv(2024)
摘要
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 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.
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