SIAM Journal on Computing, Volume 49, Issue 3, Page 540-582, January 2020.
We present a general framework for stochastic online maximization problems with combinatorial feasibility constraints. The framework establishes prophet inequalities by constructing price-based online approximation algorithms, a natural extension of threshold algorithms for settings beyond binary selection. Our analysis takes the form of an extension theorem: we derive sufficient conditions on prices when all weights are known in advance, then prove that the resulting approximation guarantees extend directly to stochastic settings. Our framework unifies and simplifies much of the existing literature on prophet inequalities and posted price mechanisms and is used to derive new and improved results for combinatorial markets (with and without complements), multidimensional matroids, and sparse packing problems. Finally, we highlight a surprising connection between the smoothness framework for bounding the price of anarchy of mechanisms and our framework, and show that many smooth mechanisms can be recast as posted price mechanisms with comparable performance guarantees.

中文翻译：

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先知不等式变得轻松：通过对非随机输入进行定价来进行随机优化

SIAM计算杂志，第49卷，第3期，第540-582页，2020年1月。
我们提出了具有组合可行性约束的随机在线最大化问题的通用框架。该框架通过构建基于价格的在线逼近算法来建立先知不等式，这是阈值算法的自然扩展，适用于除二进制选择之外的设置。我们的分析采用扩展定理的形式：当提前知道所有权重时，我们就价格得出充分条件，然后证明所得的近似保证直接扩展到随机设置。我们的框架统一并简化了许多有关先知不平等和已发布价格机制的现有文献，并用于为组合市场（有或没有补码），多维拟阵和稀疏包装问题得出新的和改进的结果。最后，