On the Curved Geometry of Accelerated Optimization

November 18, 2019

Abstract

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.

Download the Paper

AUTHORS

Written by

Aaron Defazio

Publisher

NeurIPS

Research Topics

Speech & Audio

Natural Language Processing (NLP)

Related Publications

April 17, 2025

HUMAN & MACHINE INTELLIGENCE

CONVERSATIONAL AI

Collaborative Reasoner: Self-improving Social Agents with Synthetic Conversations

Ansong Ni, Ruta Desai, Yang Li, Xinjie Lei, Dong Wang, Ramya Raghavendra, Gargi Ghosh, Daniel Li (FAIR), Asli Celikyilmaz

April 17, 2025

Read the Paper

April 17, 2025

ROBOTICS

RESEARCH

Locate 3D: Real-World Object Localization via Self-Supervised Learning in 3D

Paul McVay, Sergio Arnaud, Ada Martin, Arjun Majumdar, Krishna Murthy Jatavallabhula, Phillip Thomas, Ruslan Partsey, Daniel Dugas, Abha Gejji, Alexander Sax, Vincent-Pierre Berges, Mikael Henaff, Ayush Jain, Ang Cao, Ishita Prasad, Mrinal Kalakrishnan, Mike Rabbat, Nicolas Ballas, Mido Assran, Oleksandr Maksymets, Aravind Rajeswaran, Franziska Meier