新的优化方法在流形上实现了曲率无关的遗憾界限

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-15 04:00

研究人员开发了一种在Hadamard流形上进行去中心化在线优化的新方法，特别解决了先前方法中与曲率依赖性相关的挑战。这项工作引入了分布式黎曼在线梯度下降（D-ROGD），该方法对h-凸和强h-凸目标实现了曲率无关的遗憾界限。该方法结合了本地更新和Fréchet平均共识机制，分别产生了O(sqrt(T))和O(log T)的静态遗憾率，这与欧几里得速率相匹配，并且仅取决于网络的谱隙。双曲嵌入的实验结果验证了这些理论发现。 AI

影响在适用于在非欧几里得空间中运行的机器学习模型的优化技术方面引入了理论进展。

排序理由详细介绍一种新的理论优化方法的学术论文。[lever_c_demoted from research: ic=1 ai=1.0]

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arXiv cs.LG TIER_1 English(EN) · Zhanyuan Cai, Emre Sahinoglu, Shahin Shahrampour · 2026-09-15 04:00

Hadamard流形上分布式在线优化的曲率无关遗憾界限

arXiv:2609.13646v1 Announce Type: new Abstract: This work addresses decentralized online Riemannian optimization on Hadamard manifolds. Prior work under geodesic convexity (g-convexity) may require curvature information in the optimization analysis, typically through a finite low…

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Hadamard流形上分布式在线优化的曲率无关遗憾界限

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