Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training

TL;DR

This paper introduces a class of multi-level optimization algorithms that do not require objective function evaluations, aiming to reduce noise sensitivity and computational costs, with applications to neural network training.

Contribution

It proposes a novel multi-level, objective-function-free optimization framework, including the AdaGrad method, for more noise-robust and efficient neural network training.

Findings

Algorithms are less sensitive to noise.

Reduced computational complexity demonstrated.

Effective in deep neural network training.

Abstract

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.