First Order Bayesian Optimization (FOBO) is a sample efficient sequential approach to find the global maxima of an expensive-to-evaluate black-box objective function by suitably querying for the function and its gradient evaluations. Such methods assume Gaussian process (GP) models for both, the function and its gradient, and use them to construct an acquisition function that identifies the next query point. In this paper, we propose a class of practical FOBO algorithms that efficiently utilizes the information from the gradient GP to identify potential query points with zero gradients. We construct a multi-level acquisition function where in the first step, we optimize a lower level acquisition function with multiple restarts to identify potential query points with zero gradient value. We then use the upper level acquisition function to rank these query points based on their function values to potentially identify the global maxima. As a final step, the potential point of maxima is chosen as the actual query point. We validate the performance of our proposed algorithms on several test functions and show that our algorithms outperform state-of-the-art FOBO algorithms. We also illustrate the application of our algorithms in finding optimal set of hyper-parameters in machine learning and in learning the optimal policy in reinforcement learning tasks.

翻译：一阶贝叶斯优化（FOBO）是一种样本高效的序列化方法，通过适当查询黑箱目标函数及其梯度评估，寻找评估代价高昂的全局最大值。该方法假设函数及其梯度均服从高斯过程（GP）模型，并利用这些模型构建采集函数以确定下一个查询点。本文提出一类实用FOBO算法，可高效利用梯度GP信息识别梯度为零的潜在查询点。我们构建了多级采集函数：首先，通过多次重启优化低级采集函数，识别梯度为零的候选查询点；随后，利用高级采集函数根据函数值对这些候选点排序，以定位潜在全局最大值。最终，将候选最大值点作为实际查询点。在多个测试函数上验证了所提算法的性能，结果表明其优于现有最优FOBO算法。此外，我们展示了该算法在机器学习超参数优化及强化学习策略学习任务中的应用。