The Implicit Bias of AdaGrad on Separable Data

Part of Advances in Neural Information Processing Systems 32 (NeurIPS 2019)

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Qian Qian, Xiaoyuan Qian


We study the implicit bias of AdaGrad on separable linear classification problems. We show that AdaGrad converges to a direction that can be characterized as the solution of a quadratic optimization problem with the same feasible set as the hard SVM problem. We also give a discussion about how different choices of the hyperparameters of AdaGrad may impact this direction. This provides a deeper understanding of why adaptive methods do not seem to have the generalization ability as good as gradient descent does in practice.