可分逻辑回归边缘稳定过渡时间界研究

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   arXiv · Statistics Machine Learning

   可分逻辑回归在边缘稳定区间的紧过渡时间界

   本文研究线性可分数据上梯度下降配合大常数步长 $\eta$ 的逻辑回归动力学，分析其边缘稳定现象下的过渡时间界。现有工作在 $d=2$ 时给出 $\Theta(1)$ 界并猜想任意维度 $d\geq2$ 存在与 $\eta$ 无关的界，本文通过构造匹配困难实例，证明该猜想不成立，最坏情况过渡时间为 $\Theta((\log\eta)^{\min\{n-2,d-2\}})$。

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