We consider a deep neural network estimator based on empirical risk minimization with l_1-regularization. We derive a general bound for its excess risk in regression and classification (including multiclass), and prove that it is adaptively nearly-minimax (up to log-factors) simultaneously across the entire range of various function classes.

翻译：本文考虑一种基于经验风险最小化与l_1正则化的深度神经网络估计器。我们推导了该估计器在回归与分类（包括多分类）任务中超额风险的一般界，并证明其能在各类函数空间的完整范围内同时自适应地达到近极小化最优（仅相差对数因子）。