  Bayesian optimization (BO) is widely used to optimize expensive-to-evaluate
black-box functions.BO first builds a surrogate model to represent the
objective function and assesses its uncertainty. It then decides where to
sample by maximizing an acquisition function (AF) based on the surrogate model.
However, when dealing with high-dimensional problems, finding the global
maximum of the AF becomes increasingly challenging. In such cases, the
initialization of the AF maximizer plays a pivotal role, as an inadequate setup
can severely hinder the effectiveness of the AF.
  This paper investigates a largely understudied problem concerning the impact
of AF maximizer initialization on exploiting AFs' capability. Our large-scale
empirical study shows that the widely used random initialization strategy often
fails to harness the potential of an AF. In light of this, we propose a better
initialization approach by employing multiple heuristic optimizers to leverage
the historical data of black-box optimization to generate initial points for
the AF maximize. We evaluate our approach with a range of heavily studied
synthetic functions and real-world applications. Experimental results show that
our techniques, while simple, can significantly enhance the standard BO and
outperform state-of-the-art methods by a large margin in most test cases.
