English(EN) Mirror Descent on Riemannian Manifolds

新的镜像下降框架将优化扩展到黎曼流形

作者 PulseAugur 编辑部 · [1 个来源] · 2026-06-12 04:00

研究人员开发了一个广义的黎曼流形上镜像下降（MD）框架，将其适用性扩展到复杂的优化问题。这个新的黎曼镜像下降（RMD）框架包含一个随机变体，并提供非渐近收敛保证。当应用于Stiefel流形时，RMD框架简化为曲边梯度下降（CGD），其随机扩展有效地解决了大规模流形优化问题。 AI

排序理由这是一篇在arXiv上发表的研究论文，详细介绍了一种新的优化数学框架。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv stat.ML TIER_1 English(EN) · Jiaxin Jiang, Lei Shi, Jiyuan Tan · 2026-06-12 04:00

黎曼流形上的镜像下降

arXiv:2603.17527v2 Announce Type: replace Abstract: Mirror Descent (MD) is a scalable first-order method widely used in large-scale optimization, with applications in image processing, policy optimization, and neural network training. This paper generalizes MD to optimization on …