This paper proposes a second-order stochastic algorithm called Accelerated Double-Sketching Subspace Newton (ADSSN) to solve large-scale optimization problems with high dimensional feature spaces and substantial sample sizes. The proposed ADSSN has two computational superiority. First, ADSSN achieves a fast local convergence rate by exploiting Nesterov’s acceleration technique. Second, by taking full advantage of the double sketching strategy, ADSSN provides a lower computational cost for each iteration than competitive approaches. Moreover, these advantages hold for actually all sketching techniques, which enables practitioners to design custom sketching methods for specific applications. Finally, numerical experiments are carried out to demonstrate the efficiency of ADSSN compared with accelerated gradient descent and two single sketching counterparts.

中文翻译：

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加速双草图子空间牛顿

本文提出了一种称为加速双草绘子空间牛顿（ADSSN）的二阶随机算法，用于解决具有高维特征空间和大量样本量的大规模优化问题。所提出的 ADSSN 有两个计算优势。首先，ADSSN 通过利用 Nesterov 的加速技术实现快速的局部收敛速度。其次，通过充分利用双草图策略，ADSSN 为每次迭代提供比竞争方法更低的计算成本。此外，这些优点实际上适用于所有素描技术，这使得从业者能够为特定应用设计自定义素描方法。最后，进行数值实验以证明 ADSSN 与加速梯度下降和两个单一草图对应物相比的效率。