Optimal Regularization Can Mitigate Double Descent
This addresses a foundational problem in machine learning generalization for researchers and practitioners, offering a potential solution to non-monotonic performance issues, though it is incremental as it builds on existing regularization methods.
The paper tackles the double-descent phenomenon in learning algorithms by showing that optimal ℓ₂ regularization can mitigate it, proving monotonic test performance for linear regression with isotropic data and demonstrating empirical mitigation for neural networks.
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.