Learning Optimal Linear Regularizers

TL;DR

This paper introduces algorithms for efficiently learning optimal regularizers that enhance model generalization by framing regularization as an upper bound on the generalization gap and optimizing hyperparameters via linear programming.

Contribution

It proposes a novel approach to hyperparameter tuning by viewing regularizers as bounds on generalization, enabling efficient computation of optimal hyperparameters with limited data.

Findings

Linear programming can compute optimal regularizer hyperparameters.

Under Bayesian assumptions, the method quickly finds near-optimal hyperparameters.

Effective on both real and synthetic datasets.

Abstract

We present algorithms for efficiently learning regularizers that improve generalization. Our approach is based on the insight that regularizers can be viewed as upper bounds on the generalization gap, and that reducing the slack in the bound can improve performance on test data. For a broad class of regularizers, the hyperparameters that give the best upper bound can be computed using linear programming. Under certain Bayesian assumptions, solving the LP lets us "jump" to the optimal hyperparameters given very limited data. This suggests a natural algorithm for tuning regularization hyperparameters, which we show to be effective on both real and synthetic data.