发表机构
University of Southern California; Northwestern University; Data Science Institute at the University of Chicago; University of Chicago（南加州大学; 西北大学; 芝加哥大学数据科学研究所; 芝加哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对受LLM推理规模扩展等并行随机搜索问题启发的批量潘多拉魔盒问题，证明其近似的NP-难性后，通过线性规划松弛结合取整方法得到两种场景下的常数近似算法。
AI 中文摘要
受众多可并行化随机搜索问题的启发，其中最显著且及时的是大语言模型（LLM）推理时的规模扩展，我们提出并研究了Weitzman提出的潘多拉魔盒问题的批量版本。具体而言，魔盒在容量受限的批次中被打开，每个批次有一个设置成本，且一个批次中的所有奖励会被同时揭示。我们考虑两种不同的变体，对应不同的应用环境：一种是魔盒可重复使用（即能提供多个独立同分布样本），另一种则不可重复使用。对于这两种变体，我们排除了大多数“简单”的自然启发式算法，还正式证明了传统意义上该问题近似的NP-难性。随后，我们放宽问题以允许双准则近似，即同时针对奖励和设置成本，我们为可重复使用和不可重复使用两种场景都提出了常数近似算法。这一结果是通过对潘多拉魔盒问题进行线性规划松弛，再结合随机取整或Pipage取整得到的。
英文摘要
Motivated by numerous parallelizable stochastic search problems, most notable and timely among them being LLM inference-time scaling, we propose and study batched versions of the Pandora's Box problem of Weitzman. In particular, boxes are opened in capacity-constrained batches, each batch has a setup cost, and all rewards in a batch are revealed together. We consider two different variants, motivated by different application environments: one where boxes are reusable (i.e., can provide multiple i.i.d.~samples) and another where they are not. For both variants we rule out most ``simple'' natural heuristics, and also formally prove NP-hardness of approximation in the traditional sense. We then relax the problem to allow bi-criteria approximations, with respect to both rewards and setup costs, where we exhibit constant approximation algorithms for both the reusable and non-reusable settings. This is obtained through a linear-programming relaxation of Pandora's Box problem, followed by randomized or Pipage rounding.
