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arXiv · 2606.29186

Computing Lewis weights to high precision using local relative smoothness

Sander Gribling·Aaron Sidford·Chenyi Zhang
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Abstract

We provide algorithms that compute $\epsilon$-estimates of the $\ell_p$-Lewis weights of a matrix $A \in \mathbb{R}^{m \times n}$ for $p \geq 4$ using $O(p^2 \log(m/\epsilon))$ rounds of leverage score computation, where $\ell_p$-Lewis weights and leverage scores are both standard measures of row importance. This improves upon the state-of-the-art round complexity of $O(p^3 \log(m/\epsilon))$ due to Fazel, Lee, Padmanabha, and Sidford (2022). We obtain our results by carefully applying a local variant of relatively smooth gradient descent to primal and dual forms of the $\ell_p$-Lewis weight optimization problem and providing tools to convert between different notions of approximate $\ell_p$-Lewis weights.

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Sander Gribling, Aaron Sidford, Chenyi Zhang. 2026-06-28. Computing Lewis weights to high precision using local relative smoothness. https://arxiv.org/abs/2606.29186

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