单样本先知不等式：从组合到单项的归约
Single-Sample Prophet Inequalities: A Combinatorial to Single-Item Reduction
- The University of Texas at Austin（德克萨斯大学奥斯汀分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出从组合到单项先知不等式的通用归约，利用自由处置价值分离约束，在Googol模型下为XOS估值和可分割资源获得改进的竞争比，并给出分数背包的最优结果。
AI中文摘要：
我们研究在线组合分配中的单样本先知不等式。我们的主要贡献是一个通用归约，将组合先知不等式归约为单项先知不等式，适用于具有合适支撑价格的估值类别。该归约利用自由处置价值将买方侧组合约束与物品侧供给约束分离，形成一个模块化框架，适用于更强的Googol博弈模型。该框架为XOS估值提供了竞争比为$\frac{1}{6\sqrt{3}}\approx\frac{1}{10.4}$的单样本先知不等式，以及竞争比为$(\beta_{k-1}/4)$的$k$样本先知不等式，其中$\beta_k$是$k$样本单项先知不等式的竞争比，改进了[DKL+24]的工作。这两个结果直接扩展到具有封顶XOS估值的可分割资源。在此过程中，我们在Googol博弈模型中获得了在线自由处置的新结果，以及分数背包问题的最优单样本先知不等式。
英文摘要：
We study single-sample prophet inequalities for online combinatorial allocation. Our main contribution is a general reduction from combinatorial to single-item prophet inequalities for valuation classes admitting suitable supporting prices. The reduction uses a free-disposal value to separate buyer-side combinatorial constraints from item-side supply constraints, yielding a modular framework that applies in the stronger Game of Googol model. This framework yields a $\frac{1}{6\sqrt{3}}\approx\frac{1}{10.4}$-competitive single-sample prophet inequality and a $(β_{k-1}/4)$-competitive $k$-sample prophet inequality for XOS valuations, where $β_k$ is the competitive ratio of a $k$-sample single-item prophet inequality, improving upon the work of [DKL+24]. Both results extend directly to divisible resources with capped-XOS valuations. Along the way, we obtain new results for online free disposal and an optimal single-sample prophet inequality for fractional knapsack in the Game of Googol model.
