论文标题
随机双坐标增量聚合梯度方法的线性收敛
Linear convergence of random dual coordinate incremental aggregated gradient methods
论文作者
论文摘要
在本文中，我们考虑最小化$ \ sum_ {i \ in I} f_i（x_i）+\ sum_ {j \ in J} g_j（\ Mathcal {a} _jx）$的双重公式，in Index sets $ i $和$ j $很大。 To address the difficulties from the high dimension of the variable $x$ (i.e., $I$ is large) and the large number of component functions $g_j$ (i.e., $J$ is large), we propose a hybrid method called the random dual coordinate incremental aggregated gradient method by blending the random dual block coordinate descent method and the proximal incremental aggregated gradient method.据我们所知，没有进行任何研究以这种方式同时解决这两个困难。基于新建立的下降型引理，我们表明，在错误界限下，可以保持经典近端方法的线性收敛，甚至可以保持延迟梯度信息和随机更新坐标块。提出了三个申请示例，以证明该方法的前景。
In this paper, we consider the dual formulation of minimizing $\sum_{i\in I}f_i(x_i)+\sum_{j\in J} g_j(\mathcal{A}_jx)$ with the index sets $I$ and $J$ being large. To address the difficulties from the high dimension of the variable $x$ (i.e., $I$ is large) and the large number of component functions $g_j$ (i.e., $J$ is large), we propose a hybrid method called the random dual coordinate incremental aggregated gradient method by blending the random dual block coordinate descent method and the proximal incremental aggregated gradient method. To the best of our knowledge, no research is done to address the two difficulties simultaneously in this way. Based on a newly established descent-type lemma, we show that linear convergence of the classical proximal gradient method under error bound conditions could be kept even one uses delayed gradient information and randomly updates coordinate blocks. Three application examples are presented to demonstrate the prospect of the proposed method.
