Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e. objective function queries) with maximal expected utility with respect to the posterior distribution of a Bayesian model, which quantifies reducible, epistemic uncertainty about query outcomes. In practice, subjectively implausible outcomes can occur regularly for two reasons: 1) model misspecification and 2) covariate shift. Conformal prediction is an uncertainty quantification method with coverage guarantees even for misspecified models and a simple mechanism to correct for covariate shift. We propose conformal Bayesian optimization, which directs queries towards regions of search space where the model predictions have guaranteed validity, and investigate its behavior on a suite of black-box optimization tasks and tabular ranking tasks. In many cases we find that query coverage can be significantly improved without harming sample-efficiency.
翻译:贝叶斯优化是一种决策不确定性的一致、普遍方法,应用领域包括多臂老虎机、主动学习和黑箱优化。贝叶斯优化在Bayesian模型的后验分布中选择决策(即目标函数查询),该模型量化了关于查询结果的可减少性认识性不确定性。在实践中,出现主观上不可信的结果时,有两个原因:1)模型配错和2)协变量转移。符合预测是一种不确定性量化方法,即使是配错的模型也有覆盖率保证,并且有一个简单的机制可以纠正协变量转移。我们提出了符合贝叶斯优化,将查询引导到搜索空间的区域,其中模型预测具有成熟的有效性,并调查其在一系列黑箱优化任务和表格排名任务中的行为。在许多情况下,我们发现可以显著提高查询覆盖率而不损害样本效率。