Despite their popularity in the field of continuous optimisation, second-order quasi-Newton methods are challenging to apply in machine learning, as the Hessian matrix is intractably large. This computational burden is exacerbated by the need to address non-convexity, for instance by modifying the Hessian's eigenvalues as in Saddle-Free Newton methods. We propose an optimisation algorithm which addresses both of these concerns - to our knowledge, the first efficiently-scalable optimisation algorithm to asymptotically use the exact (eigenvalue-modified) inverse Hessian. Our method frames the problem as a series which principally square-roots and inverts the squared Hessian, then uses it to precondition a gradient vector, all without explicitly computing or eigendecomposing the Hessian. A truncation of this infinite series provides a new optimisation algorithm which is scalable and comparable to other first- and second-order optimisation methods in both runtime and optimisation performance. We demonstrate this in a variety of settings, including a ResNet-18 trained on CIFAR-10.

提出了一个既能解决大规模的Hessian矩阵问题，又能优化非凸性的优化算法，采用了一个无限级数截断的方法，并在多种情境下进行了验证，包括在CIFAR-10上训练的ResNet-18模型。

神经网络可行的无鞍牛顿优化的Hessian-Vector乘积系列