  Information-based Bayesian optimization (BO) algorithms have achieved
state-of-the-art performance in optimizing a black-box objective function.
However, they usually require several approximations or simplifying assumptions
(without clearly understanding their effects on the BO performance) and/or
their generalization to batch BO is computationally unwieldy, especially with
an increasing batch size. To alleviate these issues, this paper presents a
novel trusted-maximizers entropy search (TES) acquisition function: It measures
how much an input query contributes to the information gain on the maximizer
over a finite set of trusted maximizers, i.e., inputs optimizing functions that
are sampled from the Gaussian process posterior belief of the objective
function. Evaluating TES requires either only a stochastic approximation with
sampling or a deterministic approximation with expectation propagation, both of
which are investigated and empirically evaluated using synthetic benchmark
objective functions and real-world optimization problems, e.g., hyperparameter
tuning of a convolutional neural network and synthesizing 'physically
realizable' faces to fool a black-box face recognition system. Though TES can
naturally be generalized to a batch variant with either approximation, the
latter is amenable to be scaled to a much larger batch size in our experiments.
