A Data-Driven Bayesian Nonparametric Approach for Black-Box Optimization
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866910344372289536 |
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| author | Wang, Haowei Zhang, Xun Ng, Szu Hui Wang, Songhao |
| author_facet | Wang, Haowei Zhang, Xun Ng, Szu Hui Wang, Songhao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_02154 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A Data-Driven Bayesian Nonparametric Approach for Black-Box Optimization Wang, Haowei Zhang, Xun Ng, Szu Hui Wang, Songhao Optimization and Control 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. |
| title | A Data-Driven Bayesian Nonparametric Approach for Black-Box Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2008.02154 |