A Data-Driven Bayesian Nonparametric Approach for Black-Box Optimization
Abstract
We present a data-driven Bayesian nonparametric approach for global optimization (DaBNO) of stochastic black-box function. The function value depends on the distribution of a random vector. However, this distribution is usually complex and hardly known in practice, and is often inferred from data (realizations of random vectors). The DaBNO accounts for the finite-data error that arises when estimating the distribution and relaxes the commonly-used parametric assumption to reduce the distribution-misspecified error. We show that the DaBNO objective formulation can converge to the true objective asymptotically. We further develop a surrogate-assisted algorithm DaBNO-K to efficiently optimize the proposed objective function based on a carefully designed kernel. Numerical experiments are conducted with several synthetic and practical problems, demonstrating the empirical global convergence of this algorithm and its finite-sample performance.
Cite
@article{arxiv.2008.02154,
title = {A Data-Driven Bayesian Nonparametric Approach for Black-Box Optimization},
author = {Haowei Wang and Xun Zhang and Szu Hui Ng and Songhao Wang},
journal= {arXiv preprint arXiv:2008.02154},
year = {2024}
}