Efficient Batch Black-box Optimization with Deterministic Regret Bounds

In this work, we investigate black-box optimization from the perspective of frequentist kernel methods. We propose a novel batch optimization algorithm to jointly maximize the acquisition function and select points from a whole batch in a holistic way. Theoretically, we derive regret bounds for both the noise-free and perturbation settings. Moreover, we analyze the property of the adversarial regret that is required by robust initialization for Bayesian Optimization (BO), and prove that the adversarial regret bounds decrease with the decrease of covering radius, which provides a criterion for generating (initialization point set) to minimize the bound. We then propose fast searching algorithms to generate a point set with a small covering radius for the robust initialization. Experimental results on both synthetic benchmark problems and real-world problems show the effectiveness of the proposed algorithms.