Applications of fractional calculus in learned optimization

TL;DR

This paper explores using neural networks to adaptively predict fractional orders in fractional gradient descent, enhancing optimization in complex landscapes with non-linearities and chaotic dynamics.

Contribution

It introduces a method to train neural networks for predicting fractional orders, addressing the challenge of fine-tuning fractional derivatives in optimization.

Findings

Neural networks can effectively predict fractional orders for gradient descent.

Adaptive fractional gradient descent improves navigation of complex optimization landscapes.

The approach handles non-linearities and chaotic dynamics more robustly.

Abstract

Fractional gradient descent has been studied extensively, with a focus on its ability to extend traditional gradient descent methods by incorporating fractional-order derivatives. This approach allows for more flexibility in navigating complex optimization landscapes and offers advantages in certain types of problems, particularly those involving non-linearities and chaotic dynamics. Yet, the challenge of fine-tuning the fractional order parameters remains unsolved. In this work, we demonstrate that it is possible to train a neural network to predict the order of the gradient effectively.