带容差机构同时合成的光滑性
Smoothness for Simultaneous Composition of Mechanisms with Admission
摘要：
我们研究了入学机制中学习成果的社会福利。在我们的重复博弈中，有$n$投标人和$m$机制，并且在每一轮中，每个机制仅以一定的概率对每个投标人可用。我们的场景是一个基本的情况下，简单的机制设计与不完整的信息，可用性是投标人类型。它捕获了供应有限的在线市场中的自然应用，并可用于对无线网络中不可靠信道的访问进行建模。如果机制满足平滑保证，现有的结果表明，学习成果恢复的最优社会福利的显着部分。然而，这些方法在可扩展性和计算复杂性方面具有严重的缺点。此外，只有在投标人之间的可用性是随机独立的情况下，这些保证才适用。相比之下，我们提出了一种替代方法，每个投标人使用一个单一的无遗憾学习算法，并将其应用在所有回合。这导致了我们所说的可用性无关的粗相关均衡。它以指数方式降低了学习负担，简化了实现（例如，作为用于无线设备中的信道接入的方法），并且由此解决了关于贝叶斯设置中的贝叶斯-纳什均衡和学习结果的一些问题。我们的主要结果是一般的复合定理光滑机制时，投标人的估价函数是格次模。他们依赖于一个有趣的连接的概念相关差距的次模功能的产品格。
英文摘要：
We study social welfare of learning outcomes in mechanisms with admission. In our repeated game there are $n$ bidders and $m$ mechanisms, and in each round each mechanism is available for each bidder only with a certain probability. Our scenario is an elementary case of simple mechanism design with incomplete information, where availabilities are bidder types. It captures natural applications in online markets with limited supply and can be used to model access of unreliable channels in wireless networks. If mechanisms satisfy a smoothness guarantee, existing results show that learning outcomes recover a significant fraction of the optimal social welfare. These approaches, however, have serious drawbacks in terms of plausibility and computational complexity. Also, the guarantees apply only when availabilities are stochastically independent among bidders. In contrast, we propose an alternative approach where each bidder uses a single no-regret learning algorithm and applies it in all rounds. This results in what we call availability-oblivious coarse correlated equilibria. It exponentially decreases the learning burden, simplifies implementation (e.g., as a method for channel access in wireless devices), and thereby addresses some of the concerns about Bayes-Nash equilibria and learning outcomes in Bayesian settings. Our main results are general composition theorems for smooth mechanisms when valuation functions of bidders are lattice-submodular. They rely on an interesting connection to the notion of correlation gap of submodular functions over product lattices.
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