Gradient descent reaches arbitrary accuracy in a fixed number of large steps on multiclass logistic regression
We show that gradient descent (GD) with step size $η$ can achieve $\varepsilon$ optimality gap on the multiclass logistic regression loss in a number of iterations $T$ that is independent of $\varepsilon$. To do so, the step size $η$ must be chosen large enough as a function of $\varepsilon$ (and properties of the linearly separable dataset), while $T$ is a constant that only depends on the data. The relevant properties of the data include the number of points and their margin (for $T$), and one additional quantity (for $η$) that turns out to be necessary in dimension $d \geq 3$. The proofs build on the known fact that, as $η\to \infty$, suitably rescaled GD becomes the perceptron algorit...
| Authors | Andreea-Alexandra Musat, Nicolas Boumal |
|---|---|
| Primary category | math.OC |
| Published | 19 October 2026 |
| Last updated at source | 19 October 2026 |
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