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Risk Comparisons in Linear Regression: Implicit Regularization Dominates Explicit Regularization
Jingfeng Wu, Peter L. Bartlett, Sham M. Kakade +2
Existing theory suggests that for linear regression problems categorized by capacity and source conditions, gradient descent (GD) is always minimax optimal, while both ridge regres…
Large Stepsizes Accelerate Gradient Descent for Regularized Logistic Regression
Jingfeng Wu, Pierre Marion, Peter Bartlett
We study gradient descent (GD) with a constant stepsize for -regularized logistic regression with linearly separable data. Classical theory suggests small stepsizes to ensu…
Minimax Optimal Convergence of Gradient Descent in Logistic Regression via Large and Adaptive Stepsizes
Ruiqi Zhang, Jingfeng Wu, Licong Lin +1
We study (GD) for logistic regression on linearly separable data with stepsizes that adapt to the current risk, scaled by a constant hyperparameter …
Large Stepsize Gradient Descent for Non-Homogeneous Two-Layer Networks: Margin Improvement and Fast Optimization
Yuhang Cai, Jingfeng Wu, Song Mei +2
The typical training of neural networks using large stepsize gradient descent (GD) under the logistic loss often involves two distinct phases, where the empirical risk oscillates i…