论文标题
部分可观测时空混沌系统的无模型预测
A Trust Region Method for the Optimization of Noisy Functions
论文作者
论文摘要
经典的信任区域方法旨在解决精确的功能和梯度信息的问题。本文考虑了上述计算中存在有限错误（或噪声）的情况，并提出了对信任区域方法进行简单修改以应对这些错误。新算法仅需要有关函数评估中错误大小的信息，并且不产生额外的计算费用。结果表明，当应用于平滑（但不一定是凸的）目标函数时，该算法的迭代访问平稳性的邻居无限频繁，并且序列的其余部分不能散布太远，如函数值所衡量。数值结果说明了经典信任区域算法在存在噪声的情况下如何失败，以及所提出的算法如何确保在这些情况下稳定的稳定进步。
Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple modification of the trust region method to cope with these errors. The new algorithm only requires information about the size of the errors in the function evaluations and incurs no additional computational expense. It is shown that, when applied to a smooth (but not necessarily convex) objective function, the iterates of the algorithm visit a neighborhood of stationarity infinitely often, and that the rest of the sequence cannot stray too far away, as measured by function values. Numerical results illustrate how the classical trust region algorithm may fail in the presence of noise, and how the proposed algorithm ensures steady progress towards stationarity in these cases.
