The Implicit Bias of AdaGrad on Separable Data
This work addresses the generalization gap between adaptive methods and gradient descent in machine learning, providing theoretical insights for researchers and practitioners, though it is incremental as it builds on existing implicit bias studies.
The paper investigates the implicit bias of AdaGrad on separable linear classification problems, showing it converges to a direction characterized by a quadratic optimization problem similar to hard SVM, and discusses how hyperparameters affect this direction to explain why adaptive methods generalize worse than gradient descent in practice.
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 might 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.