Second-order step-size tuning of SGD for non-convex optimization

TL;DR

This paper introduces Step-Tuned SGD, a second-order step-size adaptation method for non-convex optimization that improves training efficiency and accuracy in deep learning by estimating curvature with local quadratic models.

Contribution

It proposes a novel second-order step-size tuning method for SGD using local curvature estimation, enhancing convergence and performance in deep neural network training.

Findings

Faster convergence to critical points.

Better test accuracy compared to SGD, RMSprop, ADAM.

Observed loss drops during training stages.

Abstract

In view of a direct and simple improvement of vanilla SGD, this paper presents a fine-tuning of its step-sizes in the mini-batch case. For doing so, one estimates curvature, based on a local quadratic model and using only noisy gradient approximations. One obtains a new stochastic first-order method (Step-Tuned SGD), enhanced by second-order information, which can be seen as a stochastic version of the classical Barzilai-Borwein method. Our theoretical results ensure almost sure convergence to the critical set and we provide convergence rates. Experiments on deep residual network training illustrate the favorable properties of our approach. For such networks we observe, during training, both a sudden drop of the loss and an improvement of test accuracy at medium stages, yielding better results than SGD, RMSprop, or ADAM.