A Quasipolynomial Algorithm for $\ell_\infty$ Contractions

Ashkan Soleymani; Gabriele Farina

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arXiv · 2610.30122

A Quasipolynomial Algorithm for $\ell_\infty$ Contractions

Ashkan Soleymani·Gabriele Farina

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Abstract

We give an algorithm for computing an $\eps$-approximate fixed point of any $d$-dimensional nonexpansion with respect to the $\ell_\infty$ norm in time $\log(1/\eps)^{O(\log^2 d)}$. At its core, our method uses a boosting argument to geometrically shrink a search region. Among other consequences, our algorithm implies that simple stochastic games can be solved in quasipolynomial time.

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Ashkan Soleymani, Gabriele Farina. 2026-10-21. A Quasipolynomial Algorithm for $\ell_\infty$ Contractions. https://arxiv.org/abs/2610.30122

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