Gaussian processes are cemented as the model of choice in Bayesian optimization and active learning. Yet, they are severely dependent on cleverly chosen hyperparameters to reach their full potential, and little effort is devoted to finding the right hyperparameters in the literature. We demonstrate the impact of selecting good hyperparameters for GPs and present two acquisition functions that explicitly prioritize this goal. Statistical distance-based Active Learning (SAL) considers the average disagreement among samples from the posterior, as measured by a statistical distance. It is shown to outperform the state-of-the-art in Bayesian active learning on a number of test functions. We then introduce Self-Correcting Bayesian Optimization (SCoreBO), which extends SAL to perform Bayesian optimization and active hyperparameter learning simultaneously. SCoreBO learns the model hyperparameters at improved rates compared to vanilla BO, while outperforming the latest Bayesian optimization methods on traditional benchmarks. Moreover, the importance of self-correction is demonstrated on an array of exotic Bayesian optimization tasks

翻译：高斯过程已被确立为贝叶斯优化和主动学习中的首选模型。然而，其性能严重依赖于精心选择的超参数才能充分发挥潜力，而现有文献中鲜有研究致力于寻找合适的超参数。我们论证了为高斯过程选择良好超参数的重要性，并提出两种明确优先考虑此目标的数据采集函数。基于统计距离的主动学习（SAL）通过统计距离度量后验样本间的平均分歧程度。实验表明，该函数在多个测试函数上的贝叶斯主动学习性能优于现有最优方法。我们进一步提出自校正贝叶斯优化（SCoreBO），该方法将SAL扩展至同步执行贝叶斯优化与主动超参数学习。与标准贝叶斯优化相比，SCoreBO能以更快的速率学习模型超参数，同时在传统基准测试中超越最新贝叶斯优化方法。此外，在一系列特殊贝叶斯优化任务中，我们验证了自校正机制的重要性。