Neural Information Processing Systems (NeurIPS)
In this work we propose a differential geometric motivation for Nesterov’s accelerated gradient method (AGM) for strongly-convex problems. By considering the optimization procedure as occurring on a Riemannian manifold with a natural structure, The AGM method can be seen as the proximal point method applied in this curved space. This viewpoint can also be extended to the continuous time case, where the accelerated gradient method arises from the natural block-implicit Euler discretization of an ODE on the manifold. We provide an analysis of the convergence rate of this ODE for quadratic objectives.
Donglai Xiang, Timur Bagautdinov, Tuur Stuyck, Fabian Prada, Javier Romero, Weipeng Xu, Shunsuke Saito, Jingfan Guo, Breannan Smith, Takaaki Shiratori, Yaser Sheikh, Jessica Hodgins, Chenglei Wu
Ludwig Sidenmark, Mark Parent, Chi-Hao Wu, Joannes Chan, Michael Glueck, Daniel Wigdor, Tovi Grossman, Marcello Giordano
Xingyi Zhou, Rohit Girdhar, Armand Joulin, Philipp Krähenbühl, Ishan Misra
