在多指标评估中高效识别最优解集，兼顾相关性与计算效率。
Pareto Set Identification With Posterior Sampling
- 基于后验采样设计停机与采样规则，联合处理结构与相关性。
- 在真实与合成数据上均表现良好，理论证明渐近最优。
- 适合多目标优化场景，尤其适用于高维相关指标问题。
从具有实值分布的候选集中识别最优解的问题已得到充分研究。然而，在存在多个可能冲突的评估指标时，相关研究较少。帕累托集识别（PSI）旨在找出其均值不被其他解全面劣化的解集。本文研究了在可传递线性设定下、具有潜在相关目标的帕累托集识别问题。基于后验采样设计停止与采样规则，提出PSIPS算法，无需支付现有基于查询的算法的计算代价即可同时处理结构与相关性。从频率学派和贝叶斯视角出发，该算法均达到渐近最优。在真实世界与合成实例中均展现出良好的经验性能。
原文摘要 · Abstract (English)
The problem of identifying the best answer among a collection of items having real-valued distribution is well-understood. Despite its practical relevance for many applications, fewer works have studied its extension when multiple and potentially conflicting metrics are available to assess an item's quality. Pareto set identification (PSI) aims to identify the set of answers whose means are not uniformly worse than another. This paper studies PSI in the transductive linear setting with potentially correlated objectives. Building on posterior sampling in both the stopping and the sampling rules, we propose the PSIPS algorithm that deals simultaneously with structure and correlation without paying the computational cost of existing oracle-based algorithms. Both from a frequentist and Bayesian perspective, PSIPS is asymptotically optimal. We demonstrate its good empirical performance in real-world and synthetic instances.
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。