In recent years, Bayesian optimization has proven successful for global optimization of expensive-to-evaluate multimodal objective functions. However, unlike most optimization methods, Bayesian optimization typically does not use derivative information. In this paper we show how Bayesian optimization can exploit derivative information to decrease the number of objective function evaluations required for good performance. In particular, we develop a novel Bayesian optimization algorithm, the derivative-enabled knowledge-gradient (dKG), for which we show one-step Bayes-optimality, asymptotic consistency, and greater one-step value of information than is possible in the derivative-free setting. Our procedure accommodates noisy and incomplete derivative information, and comes in both sequential and batch forms. We show dKG provides state-of-the-art performance compared to a wide range of optimization procedures with and without gradients, on benchmarks including logistic regression, kernel learning, and k-nearest neighbors.

本文提出了一种新的贝叶斯优化算法，它利用导数信息来降低目标函数评估的数量，可以适用于包括逐步和批量形式在内的嘈杂和不完整的导数信息，并且可以自动选择保留方向导数以减少推论的计算成本，该算法在众多优化过程中表现出最新的状态性能。

梯度贝叶斯优化