Ashkan Soleymani, Gabriele Farina · 2026 · arXiv
DOI: 10.48550/arXiv.2610.30122 · open-access PDF
Мы даем алгоритм для вычисления $\eps$-приблизительной фиксированной точки любого $d$-мерного нерасширения по отношению к $\ell_\infty$ норме во времени $\log(1/\eps)^O(\log^2 d)}$. В его основе наш метод использует аргумент повышения, чтобы геометрически сузить регион поиска.
Machine translation (Meta M2M100); the English original follows.
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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