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English(EN) Tight $L_\infty$ Sample Complexity for Low-Degree and Sparse Boolean Polynomials

新研究确立了最小-最大优化的PPAD-硬性

作者 PulseAugur 编辑部 · [4 个来源] ·

研究人员在涉及二次多项式的最小-最大优化问题方面取得了新的理论硬性结果。这些发现表明，即使在多项式、单项式出现次数有限等特定约束下，在超立方体上计算近似驻点也是PPAD-硬的。这种复杂性也延伸到双人零和多项式矩阵博弈。另外，一项关于在亚高斯噪声下学习布尔超立方体上的多项式代理的研究，刻画了最小-最大样本复杂度，显示其对于d次多项式的复杂度为n^(d+1)，对于s稀疏的傅里叶-沃尔什多项式的复杂度为ns^2。 AI

排序理由 该集群包含两篇在arXiv上发表的学术论文，详细介绍了理论计算机科学和机器学习的研究。

在 arXiv stat.ML 阅读 →

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新研究确立了最小-最大优化的PPAD-硬性

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该集群包含两篇在arXiv上发表的学术论文，详细介绍了理论计算机科学和机器学习的研究。
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报道来源 [4]

  1. arXiv cs.LG TIER_1 English(EN) · Martino Bernasconi, Matteo Castiglioni, Andrea Celli, Alexandros Hollender ·

    二次多项式的 Min-Max 优化复杂度

    arXiv:2606.17000v1 Announce Type: cross Abstract: We prove that computing approximate stationary points of min-max optimization over the hypercube is PPAD-hard for quadratic polynomials. This holds even when the polynomials are multilinear, each variable appears in at most three …

  2. arXiv cs.LG TIER_1 English(EN) · Alexandros Hollender ·

    二次多项式的 Min-Max 优化复杂度

    We prove that computing approximate stationary points of min-max optimization over the hypercube is PPAD-hard for quadratic polynomials. This holds even when the polynomials are multilinear, each variable appears in at most three monomials, and the approximation factor is inverse…

  3. arXiv stat.ML TIER_1 English(EN) · Jasper van Doornmalen, Mathieu Molina, Victor Verdugo, Jos\'e Verschae ·

    低度多项式和稀疏布尔多项式的紧凑 $L_\infty$ 样本复杂度

    arXiv:2606.17319v1 Announce Type: new Abstract: Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube. To ensure that optimizing the surrogate yields good solutions for the underlying…

  4. arXiv stat.ML TIER_1 English(EN) · José Verschae ·

    低度多项式和稀疏布尔多项式的紧凑 $L_\infty$ 样本复杂度

    Motivated by the optimization of bounded binary black-box functions, we study the problem of learning polynomial surrogates over the Boolean hypercube. To ensure that optimizing the surrogate yields good solutions for the underlying objective, we require uniform $L_\infty$-error …

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