论文标题
Linesearch Newton-CG方法用于凸出噪声的凸优化方法
Linesearch Newton-CG methods for convex optimization with noise
论文作者
论文摘要
本文通过LinesEarch newton-CG方法研究了严格凸出的不受限制优化问题的数值解决方案。我们专注于采用对目标函数和不精确的不精确评估以及可能的随机梯度和HESSIAN估计的方法。不需要衍生估计值以满足每次迭代的适当准确性要求，而是需要足够高的概率。关于目标函数的评估，我们首先假设目标函数评估中的噪声是绝对值的。然后，我们分析错误满足规定的动态精度要求的情况。我们为这两种情况提供了复杂性分析，并得出了预期的迭代复杂性界限。我们最终专注于有限和最小化的特定情况，该案例是机器学习应用的典型情况。
This paper studies the numerical solution of strictly convex unconstrained optimization problems by linesearch Newton-CG methods. We focus on methods employing inexact evaluations of the objective function and inexact and possibly random gradient and Hessian estimates. The derivative estimates are not required to satisfy suitable accuracy requirements at each iteration but with sufficiently high probability. Concerning the evaluation of the objective function we first assume that the noise in the objective function evaluations is bounded in absolute value. Then, we analyze the case where the error satisfies prescribed dynamic accuracy requirements. We provide for both cases a complexity analysis and derive expected iteration complexity bounds. We finally focus on the specific case of finite-sum minimization which is typical of machine learning applications.
