This paper introduces a new stochastic optimization method based on the regularized Fisher information matrix (FIM), named SOFIM, which can efficiently utilize the FIM to approximate the Hessian matrix for finding Newton's gradient update in large-scale stochastic optimization of machine learning models. It can be viewed as a variant of natural gradient descent, where the challenge of storing and calculating the full FIM is addressed through making use of the regularized FIM and directly finding the gradient update direction via Sherman-Morrison matrix inversion. Additionally, like the popular Adam method, SOFIM uses the first moment of the gradient to address the issue of non-stationary objectives across mini-batches due to heterogeneous data. The utilization of the regularized FIM and Sherman-Morrison matrix inversion leads to the improved convergence rate with the same space and time complexities as stochastic gradient descent (SGD) with momentum. The extensive experiments on training deep learning models using several benchmark image classification datasets demonstrate that the proposed SOFIM outperforms SGD with momentum and several state-of-the-art Newton optimization methods in term of the convergence speed for achieving the pre-specified objectives of training and test losses as well as test accuracy.

翻译：本文提出了一种基于正则化Fisher信息矩阵（FIM）的新型随机优化方法，命名为SOFIM。该方法能有效利用FIM逼近海森矩阵，以计算牛顿梯度更新，适用于大规模机器学习模型的随机优化。可视为自然梯度下降的变体，通过采用正则化FIM并利用谢尔曼-莫里森矩阵求逆直接计算梯度更新方向，解决了完整FIM的存储与计算难题。此外，与流行的Adam方法类似，SOFIM利用梯度的一阶矩处理因数据异构导致的跨小批量目标非平稳问题。正则化FIM与谢尔曼-莫里森矩阵求逆的应用，使其在保持与带动量的随机梯度下降（SGD）相同的空间与时间复杂度下，实现了更优的收敛速率。在多个基准图像分类数据集上对深度学习模型进行的大量实验表明，在达成预定的训练损失、测试损失及测试准确率目标时，所提SOFIM在收敛速度上优于带动量的SGD及多种先进的牛顿优化方法。