Online contention resolution schemes (OCRSs) are a central tool in Bayesian online selection and resource allocation: they convert fractional ex-ante relaxations into feasible online policies while preserving each marginal probability up to a constant factor. Despite their importance, designing (near) optimal OCRSs is often technically challenging, and many existing constructions rely on indirect reductions to prophet inequalities and LP duality, resulting in algorithms that are difficult to interpret or implement. In this paper, we introduce "stationary online contention resolution schemes (S-OCRSs)," a permutation-invariant class of OCRSs in which the distribution of the selected feasible set is independent of arrival order. We show that S-OCRSs admit an exact distributional characterization together with a universal online implementation. We then develop a general `maximum-entropy' approach to construct and analyze S-OCRSs, reducing the design of online policies to constructing suitable distributions over feasible sets. This yields a new technical framework for designing simple and possibly improved OCRSs. We demonstrate the power of this framework across several canonical feasibility environments. In particular, we obtain an improved $(3-\sqrt{5})/2$-selectable OCRS for bipartite matchings, attaining the independence benchmark conjectured to be optimal and yielding the best known prophet inequality for this setting. We also obtain a $1-\sqrt{2/(πk)} + O(1/k)$-selectable OCRS for $k$-uniform matroids and a simple, explicit $1/2$-selectable OCRS for weakly Rayleigh matroids (including all $\mathbb{C}$-representable matroids such as graphic and laminar). While these guarantees match the best known bounds, our framework also yields concrete and systematic constructions, providing transparent algorithms in settings where previous OCRSs were implicit or technically involved.

翻译：在线竞争消解方案（OCRSs）是贝叶斯在线选择与资源分配中的核心工具：它们将分数形式的先验松弛转化为可行的在线策略，同时以常数因子保持每个边际概率。尽管其重要性，设计（近）最优OCRS往往在技术上具有挑战性，许多现有构造依赖于先验不等式与线性规划对偶的间接归约，导致算法难以解释或实现。本文提出“静止在线竞争消解方案（S-OCRSs）”，即OCRS的一类排列不变子类，其中所选可行集的分布与到达顺序无关。我们证明S-OCRSs允许精确分布特征化及通用在线实现。进而发展了一种通用的“最大熵”方法来构造与分析S-OCRSs，将在线策略的设计简化为在可行集上构造合适的分布。这为设计简洁且可能改进的OCRS提供了新的技术框架。我们在若干典型可行性环境中展示了该框架的效力。特别地，针对二分图匹配，我们获得了改进的$(3-\sqrt{5})/2$-可选择性OCRS，达到了被认为最优的独立性基准，并给出了该环境下已知最优的先验不等式。针对$k$-均匀拟阵，我们获得了$1-\sqrt{2/(πk)} + O(1/k)$-可选择性OCRS；针对弱Rayleigh拟阵（包括所有$\mathbb{C}$-可表示拟阵，如图拟阵与层流拟阵），我们获得了简洁显式的$1/2$-可选择性OCRS。尽管这些保证与已知最优界匹配，我们的框架还提供了具体且系统的构造方法，在以往OCRS隐含或技术复杂的场景中给出了透明的算法。