自适应KappaSharp：用于偏好贝叶斯优化的条件数塑形

中文摘要 AI 辅助

偏好贝叶斯优化（PBO）用于优化仅能通过成对用户比较获取的目标。标准方法采用拉普拉斯近似对观测到的成对比较拟合高斯过程代理模型（PairwiseGP），并使用最优选项期望效用（EUBO）获取函数选择查询。EUBO在每一步查询新候选，生成的成对样本与前次查询无共享候选，此类对在比较图中形成孤立分量，从似然海森矩阵中移除一个自由度，导致矩阵秩亏。该缺陷是结构性的，无法通过改变代理建模方法解决。现有补救方法要么因强制比较保持连通性而浪费查询预算，要么应用均匀正则化，同时扰动已被观测比较充分约束的方向。我们提出KappaSharp，其能对海森矩阵进行对角校正以降低条件数，在先验不确定性较高处应用更大校正量；该校正仅在模型拟合步骤应用，而非查询选择步骤。还提出KappaSharp的自适应变体，仅当代理模型对近期比较有信心时才激活校正，避免在问题条件良好时进行不必要的校正。在11个基准测试（维度5至20，包括等离子医学中16维控制器调优问题）上，自适应KappaSharp优于标准PBO基线，性能提升最高达10.9%（p=0.003）。

英文摘要

Preferential Bayesian optimization (PBO) optimizes objectives accessible only through pairwise user comparisons. The standard approach fits a Gaussian process surrogate for observed pairwise comparisons (PairwiseGP) using the Laplace approximation and selects queries with the Expected Utility of Best Option (EUBO) acquisition function. EUBO queries new candidates at each step, producing pairs that share no candidates with previous queries. Each such pair forms an isolated component in the comparison graph, removing one degree of freedom from the likelihood Hessian and making it rank-deficient. This deficiency is structural and cannot be resolved by changing the surrogate modeling approach. Existing approaches to remedy this issue either waste query budget by forcing comparisons to stay connected, or apply uniform regularization that also perturbs directions already well-constrained by the observed comparisons. We propose KappaSharp that enables a diagonal correction to the Hessian to reduce its condition number, with larger corrections where the prior uncertainty is higher. The correction is only applied in the model fitting step, not query selection. An adaptive variant of KappaSharp is also presented that activates the correction only when the surrogate is confident about recent comparisons, avoiding unnecessary corrections when the problem is well-conditioned. On 11 benchmarks (5--20 dimensions), including a 16-dimensional controller tuning problem in plasma medicine, Adaptive KappaSharp outperforms the standard PBO baseline, with up to +10.9% ($p{=}0.003$).

发表机构

• University of California, Berkeley（加州大学伯克利分校）
• Wuhan University（武汉大学）

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