Iterative Regularization for Learning with Convex Loss Functions
This provides a new class of efficient regularized learning algorithms for machine learning practitioners, though it appears incremental as it builds on existing regularization frameworks.
The paper tackles supervised learning with convex loss functions by proposing iterative regularization via early stopping of subgradient methods, proving finite sample bounds on excess risk in reproducing kernel Hilbert spaces.
We consider the problem of supervised learning with convex loss functions and propose a new form of iterative regularization based on the subgradient method. Unlike other regularization approaches, in iterative regularization no constraint or penalization is considered, and generalization is achieved by (early) stopping an empirical iteration. We consider a nonparametric setting, in the framework of reproducing kernel Hilbert spaces, and prove finite sample bounds on the excess risk under general regularity conditions. Our study provides a new class of efficient regularized learning algorithms and gives insights on the interplay between statistics and optimization in machine learning.