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Extend risk-comparison framework beyond linear regression

Determine the extent to which the paper’s GD-versus-regularization comparisons extend beyond linear regression by (i) establishing the risk comparison between early-stopped gradient descent and the ℓ2-regularized empirical risk minimizer for Gaussian logistic regression, and (ii) establishing the risk comparison between mirror descent and LASSO for sparse linear regression with Gaussian covariates.

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Background

The analyses and tight comparison bounds in the paper rely on analytic formulas available for linear regression and do not directly extend to other learning problems.

To assess generality, the authors propose concrete extensions: comparing early-stopped GD to ℓ2-regularized ERM in Gaussian logistic regression, and comparing mirror descent to LASSO in sparse linear regression.

References

It is unclear to what extent our results generalize to other classes of statistical learning problems. As concrete questions, how would early-stopped GD compare to the \ell_2-regularized empirical risk minimizer for Gaussian logistic regression? How would mirror descent compare to LASSO for sparse linear regression?

— Risk Comparisons in Linear Regression: Implicit Regularization Dominates Explicit Regularization (2509.17251 - Wu et al., 21 Sep 2025) in Concluding remarks, paragraph “Beyond linear regression”