Gaussian processes are the model of choice in Bayesian optimization and active learning. Yet, they are highly dependent on cleverly chosen hyperparameters to reach their full potential, and little effort is devoted to finding good hyperparameters in the literature. We demonstrate the impact of selecting good hyperparameters for GPs and present two acquisition functions that explicitly prioritize hyperparameter learning. Statistical distance-based Active Learning (SAL) considers the average disagreement between samples from the posterior, as measured by a statistical distance. SAL outperforms the state-of-the-art in Bayesian active learning on several test functions. We then introduce Self-Correcting Bayesian Optimization (SCoreBO), which extends SAL to perform Bayesian optimization and active 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, we demonstrate the importance of self-correction on atypical Bayesian optimization tasks.

翻译：高斯过程是贝叶斯优化和主动学习中的首选模型。然而，它们高度依赖巧妙选择的超参数才能充分发挥潜力，而文献中对寻找良好超参数的投入甚少。我们证明了为高斯过程选择良好超参数的影响，并提出了两种明确优先考虑超参数学习的信息采集函数。基于统计距离的主动学习（SAL）通过统计距离度量后验采样之间的平均分歧。在多个测试函数上，SAL的性能优于贝叶斯主动学习的最新方法。随后，我们引入了自校正贝叶斯优化（SCoreBO），该方法扩展SAL以同时进行贝叶斯优化和主动学习。与标准贝叶斯优化相比，SCoreBO以更快的速度学习模型超参数，同时在传统基准测试中超越了最新的贝叶斯优化方法。此外，我们证明了自校正对非典型贝叶斯优化任务的重要性。