Characterizing Implicit Bias in Terms of Optimization Geometry
This work addresses the theoretical understanding of optimization algorithms in machine learning, which is foundational for researchers and practitioners, though it appears incremental as it builds on existing concepts of implicit bias.
The paper investigates whether the implicit bias of generic optimization methods like mirror descent can be characterized by the optimization geometry, independent of hyperparameters, for underdetermined linear regression and separable linear classification problems, showing that the global minimum reached can be described in terms of potentials or norms.
We study the implicit bias of generic optimization methods, such as mirror descent, natural gradient descent, and steepest descent with respect to different potentials and norms, when optimizing underdetermined linear regression or separable linear classification problems. We explore the question of whether the specific global minimum (among the many possible global minima) reached by an algorithm can be characterized in terms of the potential or norm of the optimization geometry, and independently of hyperparameter choices such as step-size and momentum.