We provide a new computationally-efficient class of estimators for risk minimization. We show that these estimators are robust for general statistical models: in the classical Huber epsilon-contamination model and in heavy-tailed settings. Our workhorse is a novel robust variant of gradient descent, and we provide conditions under which our gradient descent variant provides accurate estimators in a general convex risk minimization problem. We provide specific consequences of our theory for linear regression, logistic regression and for estimation of the canonical parameters in an exponential family. These results provide some of the first computationally tractable and provably robust estimators for these canonical statistical models. Finally, we study the empirical performance of our proposed methods on synthetic and real datasets, and find that our methods convincingly outperform a variety of baselines.

文章提出了一种新的，计算高效的风险极小化估计器类别，展示了它们在一般统计模型中的鲁棒性，特别地，在经典的Huber epsilon污染模型和重尾情况下。提出的核心是一种新型的鲁棒梯度下降算法，还给出了它在一般凸风险极小化问题中提供准确估计的条件，并以线性回归、逻辑回归和指数族中的规范参数估计为例。最后，在合成和实际数据集上研究了这种方法的实证表现，发现其比多种基线方法更具说服力。

通过健壮的梯度估计实现健壮的估计