A Dynamic Sampling Adaptive-SGD Method for Machine Learning

TL;DR

This paper introduces an adaptive stochastic gradient method that automatically adjusts batch size and learning rate, leveraging local curvature for efficient training of machine learning models without manual tuning.

Contribution

It presents a novel adaptive sampling and step size control method that ensures descent directions and achieves linear convergence on self-concordant functions, eliminating the need for manual hyperparameter tuning.

Findings

Outperforms fine-tuned SGD in training logistic regression and DNNs

Eliminates the need for manual learning rate tuning in SGD and ADAM

Achieves high probability of descent directions and linear convergence

Abstract

We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such directions, eliminating the need for the user to tune the learning rate. The proposed method exploits local curvature information and ensures that search directions are descent directions with high probability using an acute-angle test and can be used as a method that has a global linear rate of convergence on self-concordant functions with high probability. Numerical experiments show that this method is able to choose the best learning rates and compares favorably to fine-tuned SGD for training logistic regression and DNNs. We also propose an adaptive version of ADAM that eliminates the need to tune the base learning rate and compares favorably to fine-tuned ADAM on training DNNs. In our DNN experiments, we rarely encountered negative curvature at the current point along the step direction in DNNs.