Explicit and Implicit Graduated Optimization in Deep Neural Networks

TL;DR

This paper evaluates explicit graduated optimization with optimal noise scheduling and extends implicit graduated optimization to SGD with momentum, demonstrating improved performance in neural network training.

Contribution

It provides an experimental evaluation of explicit graduated optimization and extends implicit graduated optimization to momentum-based SGD, analyzing convergence and effectiveness.

Findings

Explicit graduated optimization's limitations are discussed.

Implicit graduated optimization benefits are demonstrated with ResNet.

Extended method improves neural network training performance.

Abstract

Graduated optimization is a global optimization technique that is used to minimize a multimodal nonconvex function by smoothing the objective function with noise and gradually refining the solution. This paper experimentally evaluates the performance of the explicit graduated optimization algorithm with an optimal noise scheduling derived from a previous study and discusses its limitations. It uses traditional benchmark functions and empirical loss functions for modern neural network architectures for evaluating. In addition, this paper extends the implicit graduated optimization algorithm, which is based on the fact that stochastic noise in the optimization process of SGD implicitly smooths the objective function, to SGD with momentum, analyzes its convergence, and demonstrates its effectiveness through experiments on image classification tasks with ResNet architectures.