A class of multi-level algorithms for unconstrained nonlinear optimization is presented which does not require the evaluation of the objective function. The class contains the momentum-less AdaGrad method as a particular (single-level) instance. The choice of avoiding the evaluation of the objective function is intended to make the algorithms of the class less sensitive to noise, while the multi-level feature aims at reducing their computational cost. The evaluation complexity of these algorithms is analyzed and their behaviour in the presence of noise is then illustrated in the context of training deep neural networks for supervised learning applications.

翻译：提出了一类用于无约束非线性优化的多层算法，该类算法无需计算目标函数。该算法族将无动量的AdaGrad方法作为其特例（单层实例）。避免目标函数计算的选择旨在降低算法对噪声的敏感性，而多层结构则致力于减少计算开销。本文分析了这些算法的评估复杂度，并在深度神经网络监督学习训练场景中验证了其含噪环境下的性能表现。