  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.
