To improve the off-sample generalization of classical procedures minimizing
the empirical risk under potentially heavy-tailed data, new robust learning
algorithms have been proposed in recent years, with generalized median-of-means
strategies being particularly salient. These procedures enjoy performance
guarantees in the form of sharp risk bounds under weak moment assumptions on
the underlying loss, but typically suffer from a large computational overhead
and substantial bias when the data happens to be sub-Gaussian, limiting their
utility. In this work, we propose a novel robust gradient descent procedure
which makes use of a smoothed multiplicative noise applied directly to
observations before constructing a sum of soft-truncated gradient coordinates.
We show that the procedure has competitive theoretical guarantees, with the
major advantage of a simple implementation that does not require an iterative
sub-routine for robustification. Empirical tests reinforce the theory, showing
more efficient generalization over a much wider class of data distributions.

该研究提出了一种新型的鲁棒梯度下降算法，采用直接对观测值施加平滑的乘性噪声，构建软截断梯度坐标之和的方式，使其具有与传统方法相当的理论保证和更高的数据分布类别广泛性能。