AI 中文总结
针对多目标贝叶斯优化中非平稳多输出GP与优化需求不匹配的问题，提出MOLRN-BO方法，通过正则化共享谱、残差校正及局部-全局决策策略，在12个基准上取得最优平均排名和稳健性能。
AI 中文摘要
多目标贝叶斯优化（MOBO）通常依赖于具有平稳核的独立高斯过程（GPs），这限制了其表示非平稳结构以及在目标之间共享信息的能力。然而，表达力强的非平稳GP并不一定能做出可靠的贝叶斯优化决策。我们针对多输出低秩非平稳（MO-LRN）GP研究了这种不匹配问题：强训练拟合可能与较大的设计外误差和乐观的采集预测共存。我们提出了MOLRN-BO，它结合了正则化共享谱代理与目标特定残差、前序均值校正和温度协方差缩放，以及具有周期性全局搜索的Pareto局部qLogEHVI优化。在12个确定性双目标基准上的实验表明，MOLRN-BO显著优于原始MO-LRN，并在九个评估算法中，在最终归一化超体积和归一化倒置世代距离方面取得了最佳平均问题排名。它还在随时优化中实现了最强的不良尾部性能，同时与领先基线保持竞争力。消融研究进一步表明，共享谱构造改善了设计外预测，局部-全局决策策略提高了优化性能，分层校准减少了系统性候选偏差。这些结果表明，当非平稳多输出代理的结构和使用被明确适应于顺序优化的需求时，它们可以提供强大且稳健的MOBO性能。
英文摘要
Multi-objective Bayesian optimization (MOBO) commonly relies on independent Gaussian processes (GPs) with stationary kernels, limiting its ability to represent nonstationary structure and share information between objectives. However, expressive nonstationary GPs do not necessarily make reliable BO decisions. We study this mismatch for the multi-output low-rank nonstationary (MO-LRN) GP: strong training fit can coexist with large off-design errors and optimistic acquisition predictions. We introduce MOLRN-BO, which combines a regularized shared-spectral surrogate with objective-specific residuals, prequential mean correction and tempered covariance scaling, and Pareto-local qLogEHVI optimization with periodic global search. Experiments on 12 deterministic bi-objective benchmarks show that MOLRN-BO substantially improves upon the original MO-LRN and achieves the best average problem ranks for final normalized hypervolume and normalized inverted generational distance among nine evaluated algorithms. It also achieves the strongest adverse-tail performance while remaining competitive with the leading baselines in anytime optimization. Ablation studies further show that the shared spectral construction improves off-design prediction, the local--global decision policy improves optimization performance, and hierarchical calibration reduces systematic candidate bias. These results demonstrate that nonstationary multi-output surrogates can deliver strong and robust MOBO performance when their structure and use are explicitly adapted to the demands of sequential optimization.
