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。
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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 …
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…
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…
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 …