论文标题
准编程编程和机器学习应用程序的自适应算法
Self-adaptive algorithms for quasiconvex programming and applications to machine learning
论文作者
论文摘要
为了在无限制的约束集上解决一类广泛的非凸编程问题，我们提供了一种自适应的阶梯尺寸策略，该策略不包括线路搜索技术，并在轻度假设下建立了通用方法的融合。具体而言，目标函数可能无法满足凸条件。与Descent Line-Search算法不同，它不需要已知的Lipschitz常数即可弄清第一步的规模。此过程的关键特征是步长的稳定减小，直到满足特定条件。特别是，它可以通过无限制的约束集为优化问题提供一种新的梯度投影方法。提出的方法的正确性通过一些计算示例的初步结果来验证。为了证明所提出的技术在大规模问题上的有效性，我们将其应用于机器学习的一些实验，例如监督功能选择，多变量逻辑回归和分类的神经网络。
For solving a broad class of nonconvex programming problems on an unbounded constraint set, we provide a self-adaptive step-size strategy that does not include line-search techniques and establishes the convergence of a generic approach under mild assumptions. Specifically, the objective function may not satisfy the convexity condition. Unlike descent line-search algorithms, it does not need a known Lipschitz constant to figure out how big the first step should be. The crucial feature of this process is the steady reduction of the step size until a certain condition is fulfilled. In particular, it can provide a new gradient projection approach to optimization problems with an unbounded constrained set. The correctness of the proposed method is verified by preliminary results from some computational examples. To demonstrate the effectiveness of the proposed technique for large-scale problems, we apply it to some experiments on machine learning, such as supervised feature selection, multi-variable logistic regressions and neural networks for classification.
