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A Quasipolynomial Algorithm for $\ell_\infty$ Contractions
arXiv:2610.30122v1 Announce Type: cross 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.
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.
Computer Science and Game Theory (cs.GT); Computational Complexity (cs.CC); Machine Learning (cs.LG); Optimization and Control (math.OC)
arXiv:2610.30122 [cs.GT]
(or arXiv:2610.30122v1 [cs.GT] for this version)
https://doi.org/10.48550/arXiv.2610.30122 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 162 words