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

The Marginal Value of Adaptive Gradient Methods in Machine Learning