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.

翻译：在具有实值分布的物品集合中识别最佳答案的问题已有深入研究。尽管该问题对许多应用具有实际意义，但在存在多个可能相互冲突的度量标准来评估物品质量时，其扩展形式的研究相对较少。帕累托集识别（PSI）旨在确定那些均值不会在所有维度上均劣于其他答案的答案集合。本文研究具有潜在相关目标的转导线性设置下的PSI问题。基于后验采样的停止规则与采样规则，我们提出PSIPS算法，该算法能同时处理结构相关性与目标相关性，且无需支付现有基于预言机算法的计算成本。无论从频率学派还是贝叶斯学派的角度分析，PSIPS均具有渐近最优性。我们在真实场景与合成实例中验证了其良好的实证性能。