论文标题
用于优化问题的梯度型方法Polyak-lojasiewicz条件：早期停止和适应不符合性参数
Gradient-Type Methods for Optimization Problems with Polyak-Łojasiewicz Condition: Early Stopping and Adaptivity to Inexactness Parameter
论文作者
论文摘要
由于其在机器学习和其他连接的工程应用中的许多不同位置的应用，因此满足Polyak-olojasiewicz条件的平滑功能的最小化问题引起了研究人员的广泛关注。最近，对于这个问题，最近工作的作者提出了一种使用不精确梯度的自适应梯度型方法。适应性仅在梯度的Lipschitz常数方面发生。在本文中，对于polyak-lojasiewicz条件的问题，我们提出了一种完整的自适应算法，这意味着适应性是相对于梯度的Lipschitz常数以及梯度中噪声水平的。我们提供了对拟议算法的收敛性的详细分析，以及从起点到算法输出点的距离估计。进行了数值实验和比较，以说明在某些示例中提出的算法的优势。
Due to its applications in many different places in machine learning and other connected engineering applications, the problem of minimization of a smooth function that satisfies the Polyak-Łojasiewicz condition receives much attention from researchers. Recently, for this problem, the authors of recent work proposed an adaptive gradient-type method using an inexact gradient. The adaptivity took place only with respect to the Lipschitz constant of the gradient. In this paper, for problems with the Polyak-Łojasiewicz condition, we propose a full adaptive algorithm, which means that the adaptivity takes place with respect to the Lipschitz constant of the gradient and the level of the noise in the gradient. We provide a detailed analysis of the convergence of the proposed algorithm and an estimation of the distance from the starting point to the output point of the algorithm. Numerical experiments and comparisons are presented to illustrate the advantages of the proposed algorithm in some examples.
