提出新型维度度量，用于推导统计与在线学习的收敛速度下界。
A Gapped Scale-Sensitive Dimension and Lower Bounds for Offset Rademacher Complexity
- 引入间隙化尺度敏感维度，刻画函数类复杂性
- 证明该维度控制有界函数类的覆盖数上界
- 为偏置Rademacher平均提供新下界，适用于理论分析
我们研究了函数类在序列与非序列设定下的间隙化尺度敏感维度。证明任意一致有界的函数类的覆盖数均被这些间隙维度所控制，推广了 extcite{anthony2000function,alon1997scale} 的结果。此外，我们表明间隙维度可导出偏置Rademacher平均的下界，从而强化了在统计学习和在线学习中证明收敛速率下界的现有方法。
原文摘要 · Abstract (English)
We study gapped scale-sensitive dimensions of a function class in both sequential and non-sequential settings. We demonstrate that covering numbers for any uniformly bounded class are controlled above by these gapped dimensions, generalizing the results of \cite{anthony2000function,alon1997scale}. Moreover, we show that the gapped dimensions lead to lower bounds on offset Rademacher averages, thereby strengthening existing approaches for proving lower bounds on rates of convergence in statistical and online learning.
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