This paper studies the effect of adding geometrically smoothed momentum to the randomized Kaczmarz algorithm, which is an instance of stochastic gradient descent on a linear least squares loss function. We prove a result about the expected error in the direction of singular vectors of the matrix defining the least squares loss. We present several numerical examples illustrating the utility of our result and pose several questions.

翻译：本文研究了在随机Kaczmarz算法（在线性最小二乘损失函数上随机梯度下降的一个实例）中添加几何平滑动量的效果。我们证明了关于该矩阵（定义最小二乘损失）奇异向量方向上期望误差的一个结果。通过若干数值算例，我们展示了该结果的实用性，并提出了若干待解问题。