SIAM Journal on Computing, Volume 50, Issue 2, Page 255-300, January 2021.
We introduce a new rounding technique designed for online optimization problems, which is related to contention resolution schemes, a technique initially introduced in the context of submodular function maximization. Our rounding technique, which we call online contention resolution schemes (OCRSs), is applicable to many online selection problems, including Bayesian online selection, oblivious posted pricing mechanisms, and stochastic probing models. It allows for handling a wide set of constraints and shares many strong properties of offline contention resolution schemes. In particular, OCRSs for different constraint families can be combined to obtain an OCRS for their intersection. Moreover, we can approximately maximize submodular functions in the online settings we consider. We thus get a broadly applicable framework for several online selection problems, which improves on previous approaches in terms of the types of constraints that can be handled, the objective functions that can be dealt with, and the assumptions on the strength of the adversary. Furthermore, we resolve two open problems from the literature; namely, we present the first constant-factor constrained oblivious posted price mechanism for matroid constraints and the first constant-factor algorithm for weighted stochastic probing with deadlines.

中文翻译：

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在线争用解决方案与贝叶斯选择问题的应用

SIAM Journal on Computing，第 50 卷，第 2 期，第 255-300 页，2021 年 1 月。
我们引入了一种为在线优化问题设计的新舍入技术，该技术与争用解决方案相关，该技术最初是在子模函数最大化的背景下引入的。我们的舍入技术，我们称之为在线竞争解决方案 (OCRS)，适用于许多在线选择问题，包括贝叶斯在线选择、不经意发布的定价机制和随机探测模型。它允许处理一系列广泛的约束并共享许多离线争用解决方案的强大属性。特别是，可以组合不同约束族的 OCRS 以获得它们的交集的 OCRS。此外，我们可以在我们考虑的在线设置中近似最大化子模块函数。因此，我们为几个在线选择问题获得了一个广泛适用的框架，它在可以处理的约束类型、可以处理的目标函数以及对对手实力的假设方面改进了以前的方法。此外，我们从文献中解决了两个未解决的问题；即，我们提出了第一个用于拟阵约束的常数因子约束不经意发布价格机制和第一个用于带期限加权随机探测的常数因子算法。