提出可精确计算的偏好型贝叶斯优化知识梯度方法
Knowledge Gradient for Preference Learning
- 推导出偏好优化中精确的解析知识梯度公式
- 在多个基准测试中表现优于现有方法
- 适用于需成对比较的黑箱优化场景
知识梯度是贝叶斯优化中一种流行的采集函数，用于优化带有噪声评估的黑箱目标函数。然而，许多实际场景仅允许成对比较查询，导致无法直接获取函数值，形成偏好型贝叶斯优化问题。将知识梯度推广到偏好型设置面临计算挑战，核心在于其前瞻步骤需计算非高斯后验分布，此前被认为不可行。本文通过推导，首次获得偏好型贝叶斯优化中精确且解析的知识梯度。实验表明，该方法在多个基准测试中表现优异，常优于现有采集函数。此外，还通过案例研究揭示了知识梯度在某些场景下的局限性。
原文摘要 · Abstract (English)
The knowledge gradient is a popular acquisition function in Bayesian optimization (BO) for optimizing black-box objectives with noisy function evaluations. Many practical settings, however, allow only pairwise comparison queries, yielding a preferential BO problem where direct function evaluations are unavailable. Extending the knowledge gradient to preferential BO is hindered by its computational challenge. At its core, the look-ahead step in the preferential setting requires computing a non-Gaussian posterior, which was previously considered intractable. In this paper, we address this challenge by deriving an exact and analytical knowledge gradient for preferential BO. We show that the exact knowledge gradient performs strongly on a suite of benchmark problems, often outperforming existing acquisition functions. In addition, we also present a case study illustrating the limitation of the knowledge gradient in certain scenarios.
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