A Quasipolynomial Algorithm for $\ell_\infty$ Contractions

The paper presents a quasipolynomial-time algorithm for finding an ε-approximate fixed point of any d-dimensional nonexpansion under the λ∞ norm, running in time −log(1/ε)^{O(log^2 d)}. The method relies on a boosting argument that geometrically shrinks the search region. As a consequence, the algorithm shows that simple stochastic games can be solved in quasipolynomial time.

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