论文标题
从Nesterov的估计序列到Riemannian加速
From Nesterov's Estimate Sequence to Riemannian Acceleration
论文作者
论文摘要
我们提出了第一种用于Riemannian流形的全球加速梯度方法。为了建立我们的结果，我们重新审视Nesterov的估计序列技术，并为其开发替代分析，也可能具有独立的兴趣。然后，我们将此分析扩展到Riemannian设置，将由于非欧国人结构引起的关键难度定位到一定的``度量失真''中。我们通过制定新的几何不平等来控制这种失真，这使我们能够提出和分析Nesterov加速渐变的Riemannian对抗。
We propose the first global accelerated gradient method for Riemannian manifolds. Toward establishing our result we revisit Nesterov's estimate sequence technique and develop an alternative analysis for it that may also be of independent interest. Then, we extend this analysis to the Riemannian setting, localizing the key difficulty due to non-Euclidean structure into a certain ``metric distortion.'' We control this distortion by developing a novel geometric inequality, which permits us to propose and analyze a Riemannian counterpart to Nesterov's accelerated gradient method.
