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English(EN) Beyond the $d^{2.5}$-mixing bound for Dikin walks on polytopes

多面体上 Dikin 游走混合时间改进至 $d^{2.25}$

作者 PulseAugur 编辑部 · [2 个来源] ·

研究人员在多面体上 Dikin 游走的混合时间方面取得了进展，这是一种受凸优化内点法启发的计算方法。一篇新论文将先前 $d^{2.5}$ 的混合界限改进至 $d^{2.25}$，用于从多面体进行指数采样。这一进展依赖于对 Lee--Sidford 度量的更高阶分析，并采用了选择性高阶展开和 Wiener-chaos 分解等技术。 AI

影响 这项研究可能为机器学习和优化问题中的采样算法带来更高的效率。

排序理由 该集群包含一篇详细介绍多面体采样算法理论进展的研究论文。

在 arXiv cs.LG 阅读 →

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多面体上 Dikin 游走混合时间改进至 $d^{2.25}$

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报道来源 [2]

  1. arXiv cs.LG TIER_1 English(EN) · Yunbum Kook ·

    Beyond the $d^{2.5}$-mixing bound for Dikin walks on polytopes

    arXiv:2607.13943v1 Announce Type: cross Abstract: Inspired by interior-point methods (IPM) for structured convex optimization, Kannan and Narayanan introduced the Dikin walk for sampling uniformly from polytopes in 2009. As in IPMs, the Dikin walk is affine-invariant, and its con…

  2. arXiv cs.LG TIER_1 English(EN) · Yunbum Kook ·

    Beyond the $d^{2.5}$-mixing bound for Dikin walks on polytopes

    Inspired by interior-point methods (IPM) for structured convex optimization, Kannan and Narayanan introduced the Dikin walk for sampling uniformly from polytopes in 2009. As in IPMs, the Dikin walk is affine-invariant, and its convergence is governed by the barrier geometry used …

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