Littlestone维数和阈值维数的近紧闭包界
Near-tight closure bounds for Littlestone and threshold dimensions
摘要：
我们研究封闭性质的Littlestone和阈值尺寸的二元假设类。给定类$\mathcal{H}_1, \ldots, \mathcal{H}_k$的布尔函数有界Littlestone（分别，阈值）的维数，我们建立了一个上限上的Littlestone（分别，阈值）维数的类定义通过应用任意的二进制聚合规则$\mathcal{H}_1, \ldots, \mathcal{H}_k$。我们还表明，我们的上界几乎紧。我们的上界给出了Alon等人（COLT 2020）所示类似边界的指数（在$k$中）改进，从而回答了他们的工作提出的问题。
英文摘要：
We study closure properties for the Littlestone and threshold dimensions of binary hypothesis classes. Given classes $\mathcal{H}_1, \ldots, \mathcal{H}_k$ of Boolean functions with bounded Littlestone (respectively, threshold) dimension, we establish an upper bound on the Littlestone (respectively, threshold) dimension of the class defined by applying an arbitrary binary aggregation rule to $\mathcal{H}_1, \ldots, \mathcal{H}_k$. We also show that our upper bounds are nearly tight. Our upper bounds give an exponential (in $k$) improvement upon analogous bounds shown by Alon et al. (COLT 2020), thus answering a question posed by their work.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
