# LOSSGRAD: automatic learning rate in gradient descent

## TL;DR

LOSOGRAD is a simple, fast algorithm that automatically adjusts the learning rate during neural network training, making it more robust to initial settings while maintaining competitive performance.

## Contribution

The paper introduces LOSSGRAD, an easy-to-implement method for automatically optimizing step-size in gradient descent based on local quadratic approximation.

## Key findings

- Insensitive to initial learning rate choices
- Achieves results comparable to existing methods
- Simple and fast to implement

## Abstract

In this paper, we propose a simple, fast and easy to implement algorithm LOSSGRAD (locally optimal step-size in gradient descent), which automatically modifies the step-size in gradient descent during neural networks training. Given a function $f$, a point $x$, and the gradient $\nabla_x f$ of $f$, we aim to find the step-size $h$ which is (locally) optimal, i.e. satisfies: $$ h=arg\,min_{t \geq 0} f(x-t \nabla_x f). $$ Making use of quadratic approximation, we show that the algorithm satisfies the above assumption. We experimentally show that our method is insensitive to the choice of initial learning rate while achieving results comparable to other methods.