Optimal Regularization Can Mitigate Double Descent

TL;DR

This paper demonstrates that optimal regularization, specifically tuned $ ext{l}_2$ regularization, can eliminate the double descent phenomenon in test performance across linear models and neural networks, enhancing understanding of generalization.

Contribution

The work proves that optimal $ ext{l}_2$ regularization can ensure monotonic test performance, providing a theoretical and empirical solution to double descent.

Findings

Optimal regularization achieves monotonic test performance.

Empirical mitigation of double descent in neural networks.

Theoretical proof for linear regression models with isotropic data.

Abstract

Recent empirical and theoretical studies have shown that many learning algorithms -- from linear regression to neural networks -- can have test performance that is non-monotonic in quantities such the sample size and model size. This striking phenomenon, often referred to as "double descent", has raised questions of if we need to re-think our current understanding of generalization. In this work, we study whether the double-descent phenomenon can be avoided by using optimal regularization. Theoretically, we prove that for certain linear regression models with isotropic data distribution, optimally-tuned $\ell_2$ regularization achieves monotonic test performance as we grow either the sample size or the model size. We also demonstrate empirically that optimally-tuned $\ell_2$ regularization can mitigate double descent for more general models, including neural networks. Our results suggest that it may also be informative to study the test risk scalings of various algorithms in the context of appropriately tuned regularization.