Minimax Optimal Early-Stopped Gradient Descent for Gaussian Mixture Classification
In overparameterised classification, training data can be linearly separable even when the underlying distribution is not. In this setting, gradient descent (GD) on the logistic loss diverges in norm while converging in direction to a max-margin interpolating classifier, whose implicit bias can be statistically suboptimal. In this work, we show that early stopping can overcome this suboptimality: in a Gaussian mixture model with label-flipping noise, GD stopped at an appropriate oracle time achieves minimax-optimal excess zero-one risk for covariance spectra with fast and continuous decay, including polynomial and exponential spectral decays. Our analysis combines a sharp upper bound for ...
| Authors | Alex Buna, Shirley Xiaoqi Liu, Patrick Rebeschini |
|---|---|
| Primary category | stat.ML |
| Published | 6 August 2026 |
| Last updated at source | 6 August 2026 |
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