  Bayesian optimization (BO) is a popular approach for expensive black-box
optimization, with applications including parameter tuning, experimental
design, robotics. BO usually models the objective function by a Gaussian
process (GP), and iteratively samples the next data point by maximizing an
acquisition function. In this paper, we propose a new general framework for BO
by generating pseudo-points (i.e., data points whose objective values are not
evaluated) to improve the GP model. With the classic acquisition function,
i.e., upper confidence bound (UCB), we prove that the cumulative regret can be
generally upper bounded. Experiments using UCB and other acquisition functions,
i.e., probability of improvement (PI) and expectation of improvement (EI), on
synthetic as well as real-world problems clearly show the advantage of
generating pseudo-points.
