论文标题
可变度量和Nesterov推断近端DCA，带有复合DC程序的回溯
A Variable Metric and Nesterov Extrapolated Proximal DCA with Backtracking for A Composite DC Program
论文作者
论文摘要
在本文中，我们考虑了一个复合范围差异（DC）程序，其目标函数是具有Lipschitz连续梯度的平滑凸功能的总和，适当的闭合和凸功能以及连续的凹函数。这个问题在机器学习和数据科学中有许多应用。近端DCA（PDCA）是经典DCA的特殊情况，以及两个Nesterov型推断DCA-ADCA（Phan等人IJCAI：1369---1375，2018）和PDCAE（Wen等人Comput Optim Comput Appl Appl 69：297：297：297--324，2018）可以解决此问题。 PDCA，PDCAE和ADCA的算法级数是通过估计损耗函数的平滑度参数来固定和确定的。但是，在某些现实世界中，这种估计可能很难获得或差。在这种困难的推动下，我们提出了一个可变度量和Nesterov推断DCA与回溯（SPDCAE）的近端（SPDCAE），该指标结合了回溯线搜索程序（不一定是单调）和Nesterov的推断，并推出了Nesterov的推断;此外，将可变度量方法合并为更好的局部近似。稀疏的二元逻辑回归和用泊松噪声压缩感测的数值模拟证明了我们提出的方法的有效性。
In this paper, we consider a composite difference-of-convex (DC) program, whose objective function is the sum of a smooth convex function with Lipschitz continuous gradient, a proper closed and convex function, and a continuous concave function. This problem has many applications in machine learning and data science. The proximal DCA (pDCA), a special case of the classical DCA, as well as two Nesterov-type extrapolated DCA -- ADCA (Phan et al. IJCAI:1369--1375, 2018) and pDCAe (Wen et al. Comput Optim Appl 69:297--324, 2018) -- can solve this problem. The algorithmic step-sizes of pDCA, pDCAe, and ADCA are fixed and determined by estimating a prior the smoothness parameter of the loss function. However, such an estimate may be hard to obtain or poor in some real-world applications. Motivated by this difficulty, we propose a variable metric and Nesterov extrapolated proximal DCA with backtracking (SPDCAe), which combines the backtracking line search procedure (not necessarily monotone) and the Nesterov's extrapolation for potential acceleration; moreover, the variable metric method is incorporated for better local approximation. Numerical simulations on sparse binary logistic regression and compressed sensing with Poisson noise demonstrate the effectiveness of our proposed method.
