提出可计算的q-占优关系，实现多目标优化中更可靠的解排序。
Center-Outward q-Dominance: A Sample-Computable Proxy for Strong Stochastic Dominance in Multi-Objective Optimisation
- 基于最优传输理论构建q-占优关系，可有效判断多变量分布优劣。
- 在YAHPO-MO和ZDT测试中，相比传统方法提升排序准确性和收敛速度。
- 适合需要严格概率优势比较的多目标优化研究者使用。
随机多目标优化（SMOOP）需对多维分布进行排序；现有方法多采用标量化处理，会丢失信息且不可靠。本文基于最优传输理论，提出中心向外q-占优关系，并证明其蕴含强一阶随机占优（FSD）。我们还开发了基于q-占优的实证检验方法，推导出控制第一类错误的样本量阈值 $n^*(δ)$。在两个场景中验证了该方法的有效性：（1）作为超参数调优中的排序方法，分析七个多目标调优器在YAHPO-MO基准任务上的最终随机帕累托集，使在期望超体积指标（HVI）无法区分时仍能比较性能；（2）替换NSGA-II算法中基于均值的选择策略为q-占优，在含噪声的ZDT基准问题上展现出更优的收敛速率。结果表明，中心向外q-占优为寻找真正随机占优解提供了严谨且可计算的基础。
原文摘要 · Abstract (English)
Stochastic multi-objective optimization (SMOOP) requires ranking multivariate distributions; yet, most empirical studies perform scalarization, which loses information and is unreliable. Based on the optimal transport theory, we introduce the center-outward q-dominance relation and prove it implies strong first-order stochastic dominance (FSD). Also, we develop an empirical test procedure based on q-dominance, and derive an explicit sample size threshold, $n^*(δ)$, to control the Type I error. We verify the usefulness of our approach in two scenarios: (1) as a ranking method in hyperparameter tuning; (2) as a selection method in multi-objective optimization algorithms. For the former, we analyze the final stochastic Pareto sets of seven multi-objective hyperparameter tuners on the YAHPO-MO benchmark tasks with q-dominance, which allows us to compare these tuners when the expected hypervolume indicator (HVI, the most common performance metric) of the Pareto sets becomes indistinguishable. For the latter, we replace the mean value-based selection in the NSGA-II algorithm with $q$-dominance, which shows a superior convergence rate on noise-augmented ZDT benchmark problems. These results establish center-outward q-dominance as a principled, tractable foundation for seeking truly stochastically dominant solutions for SMOOPs.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。