标题： 关于（正则化）经验风险最小化的集中性 显示英文标题

标题： On concentration for (regularized) empirical risk minimization

摘要： 经验风险最小化器的收敛速度在文献中已经得到了很好的研究。 在本文中，我们通过证明经过归一化后，经验最小化器集中在一点上来补充这些速度。 这样的结果首先由\cite{chatterjee2014new}在最小二乘法的背景下建立。 我们将这一结果推广到其他损失函数，例如指数族的负对数似然。 我们还允许使用严格凸的正则化惩罚。 这些结果基于经验过程最大值的集中不等式。 显示英文摘要

摘要： Rates of convergence for empirical risk minimizers have been well studied in the literature. In this paper we complement the rates by showing that after normalization, the empirical minimizer concentrates on a single point. Such results have first been established by \cite{chatterjee2014new} in the least squares context. We generalize this to other loss functions such minus log-likelihood for exponential families. We furthermore allow for a strictly convex regularization penalty. The results are based on concentration inequalities for maxima of empirical processes.