论文标题
一种耐噪声的准Newton算法，用于不受约束的优化
A Noise-Tolerant Quasi-Newton Algorithm for Unconstrained Optimization
论文作者
论文摘要
本文介绍了BFGS和L-BFGS方法的扩展，以最大程度地减少受误差的非线性函数。这项工作是由包含计算噪声，采用低精度算术或受统计噪声的应用的激励。在这种情况下，经典的BFG和L-BFGS方法可能会失败，因为更新过程可能会损坏，并且行搜索可能会不正当。提出的方法解决了这些困难，并通过采用延长程序来确保BFGS更新稳定，从而使收集梯度差异的点增加了。一项新的线路搜索旨在容忍错误，可以确保在大多数合理条件下满足Armijo-Wolfe条件，并与延长过程结合使用。所提出的方法被证明可以享受强烈凸功能的融合保证。提出了这些方法的详细实现，并鼓励了数值结果。
This paper describes an extension of the BFGS and L-BFGS methods for the minimization of a nonlinear function subject to errors. This work is motivated by applications that contain computational noise, employ low-precision arithmetic, or are subject to statistical noise. The classical BFGS and L-BFGS methods can fail in such circumstances because the updating procedure can be corrupted and the line search can behave erratically. The proposed method addresses these difficulties and ensures that the BFGS update is stable by employing a lengthening procedure that spaces out the points at which gradient differences are collected. A new line search, designed to tolerate errors, guarantees that the Armijo-Wolfe conditions are satisfied under most reasonable conditions, and works in conjunction with the lengthening procedure. The proposed methods are shown to enjoy convergence guarantees for strongly convex functions. Detailed implementations of the methods are presented, together with encouraging numerical results.
