We study Stochastic Online Correlated Selection (SOCS), a family of online rounding algorithms for Non-IID Stochastic Online Submodular Welfare Maximization and special cases such as Online Stochastic Matching, Stochastic AdWords, and Stochastic Display Ads. At each step, the algorithm sees an online item's type and fractional allocation, then immediately allocates it to an agent. We propose a metric called the convergence rate for the quality of SOCS. This is cleaner than most metrics in the OCS literature. We propose a Type Decomposition that reduces SOCS to the two-way special case. First, we sample a surrogate type with half-integer allocation. The rounding is trivial for a one-way type fully allocated to an agent. For a two-way type split equally between two agents, we round it using two-way SOCS. We design the distribution of surrogate types to get two-way types as often as possible while respecting the original fractional allocation in expectation. Following this framework, we make progress on numerous problems: 1) Online Stochastic Matching: We improve the state-of-the-art $0.666$ competitive ratio for unweighted/vertex-weighted matching to $0.69$. 2) Query-Commit Matching: We enhance the ratio to $0.705$ in the Query-Commit model, improving the best previous $0.696$ and $0.662$ for unweighted and vertex-weighted matching. 3) Stochastic AdWords: We give a $0.6338$ competitive algorithm, breaking the $1-\frac{1}{e}$ barrier and answering a decade-old open question. 4) AdWords: The framework applies to the adversarial model if the rounding is oblivious to future items' distributions. We get the first multi-way OCS for AdWords, addressing an open question about OCS. This gives a $0.504$ competitive ratio for AdWords, improving the previous $0.501$. 5) Stochastic Display Ads: We design a $0.644$ competitive algorithm, breaking the $1-\frac{1}{e}$ barrier.

翻译：本文研究随机在线相关选择（SOCS），这是一类用于非独立同分布随机在线次模福利最大化及其特例（如在线随机匹配、随机广告词和随机展示广告）的在线舍入算法。在每一步，算法观测在线物品的类型和分数分配，并立即将其分配给一个智能体。我们提出了一种称为收敛率的度量标准来评估SOCS的质量，该度量比OCS文献中的大多数指标更为简洁。我们提出了一种类型分解方法，将SOCS约化为双向特例。首先，我们采样一个具有半整数分配的代理类型。对于完全分配给单个智能体的单向类型，舍入是平凡的。对于在两个智能体间均等分配的双向类型，我们使用双向SOCS进行舍入。我们设计了代理类型的分布，以在期望意义上尊重原始分数分配的同时，尽可能频繁地获得双向类型。基于此框架，我们在多个问题上取得进展：1）在线随机匹配：将未加权/顶点加权匹配的最优竞争比从0.666提升至0.69；2）查询提交匹配：在查询提交模型中，将竞争比提升至0.705，改进了先前未加权和顶点加权匹配的最佳结果0.696和0.662；3）随机广告词：提出竞争比为0.6338的算法，突破了$1-\frac{1}{e}$的界限，并回答了一个悬置十年的开放性问题；4）广告词：若舍入过程对未来物品分布不可知，该框架可应用于对抗模型。我们首次为广告词设计了多路OCS，解决了关于OCS的一个开放性问题，将广告词的竞争比从0.501提升至0.504；5）随机展示广告：设计了竞争比为0.644的算法，突破了$1-\frac{1}{e}$的界限。