The Marginal Value of Adaptive Gradient Methods in Machine Learning

TL;DR

This paper investigates the differences between adaptive gradient methods and traditional gradient descent in training neural networks, revealing that adaptive methods often find solutions with worse generalization despite good training performance.

Contribution

It provides theoretical and empirical evidence that adaptive methods can lead to solutions with poorer generalization compared to SGD, challenging their widespread use in deep learning.

Findings

Adaptive methods find solutions with worse test error than GD/SGD.

In a constructed example, adaptive methods fail to achieve zero test error.

Empirical results show adaptive methods generalize worse on real models.

Abstract

Adaptive optimization methods, which perform local optimization with a metric constructed from the history of iterates, are becoming increasingly popular for training deep neural networks. Examples include AdaGrad, RMSProp, and Adam. We show that for simple overparameterized problems, adaptive methods often find drastically different solutions than gradient descent (GD) or stochastic gradient descent (SGD). We construct an illustrative binary classification problem where the data is linearly separable, GD and SGD achieve zero test error, and AdaGrad, Adam, and RMSProp attain test errors arbitrarily close to half. We additionally study the empirical generalization capability of adaptive methods on several state-of-the-art deep learning models. We observe that the solutions found by adaptive methods generalize worse (often significantly worse) than SGD, even when these solutions have better training performance. These results suggest that practitioners should reconsider the use of adaptive methods to train neural networks.