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