Dual Space Preconditioning for Gradient Descent in the Overparameterized Regime
In this work, we study the convergence properties of the Dual Space Preconditioned Gradient Descent, encompassing optimizers such as Normalized Gradient Descent and Gradient Clipping. We consider preconditioners of the form $\nabla K$, where $K: \mathbb{R}^{d \times k} \to \mathbb{R}$ is convex and apply $\nabla K(\cdot)$ to train an over-parameterized linear model with a convex loss of the form $\ell(X W - Y)$, for weights $W \in \mathbb{R}^{d \times k}$, labels $Y \in \mathbb{R}^{n \times k}$ and data $X \in \mathbb{R}^{n \times d}$. Under the aforementioned assumptions, we prove that the iterates of the full-batch preconditioned gradient descent converge at an exponential rate to a poi...
| Authors | Reza Ghane, Danil Akhtiamov, Babak Hassibi |
|---|---|
| Primary category | stat.ML |
| Published | 11 March 2026 |
| Last updated at source | 10 August 2026 |
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