Sanyou Mei · 2026 · arXiv
DOI: 10.48550/arXiv.2610.27386 · open-access PDF
对于折扣的成本,我们为简单的战略迭代方法设定了指数级和超多元级迭代的下限,以丹西格的规则分别为不受限制的成本和单位重量。 根据我们所知,这首次表明,即使所有行动成本都属于 $\{-1,0,1\},这种方法也不具有强烈的多元性。
Machine translation (Meta M2M100); the English original follows.
We study turn-based deterministic zero-sum games with discounted and long-run average costs. For discounted costs, we establish exponential and superpolynomial iteration lower bounds for the simple strategy-iteration method with Dantzig's rule under unrestricted costs and unit weights, respectively. To the best of our knowledge, this shows for the first time that the method is not strongly polynomial even when all action costs belong to $\{-1,0,1\}$. For long-run average costs, we establish an exponential iteration lower bound for termination of a Dantzig counterpart with unrestricted costs an
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