Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent
Files
Accepted manuscript
Date
2017
Authors
Orecchia, Lorenzo
Allen-Zhu, Zeyuan
Version
Accepted manuscript
OA Version
Citation
L Orecchia, Zeyuan Allen-Zhu. "Linear Coupling: An Ultimate Unification of Gradient and Mirror Descent." Innovations in Theoretical Computer Science
Abstract
First-order methods play a central role in large-scale machine learning. Even though many variations exist, each suited to a particular problem, almost all such methods fundamentally rely on two types of algorithmic steps: gradient descent, which yields primal progress, and mirror descent, which yields dual progress. We observe that the performances of gradient and mirror descent are complementary, so that faster algorithms can be designed by "linearly coupling" the two. We show how to reconstruct Nesterov's accelerated gradient methods using linear coupling, which gives a cleaner interpretation than Nesterov's original proofs. We also discuss the power of linear coupling by extending it to many other settings that Nesterov's methods cannot apply to.
Description
License
© Zeyuan Allen-Zhu and Lorenzo Orecchia;
licensed under Creative Commons License CC-BY.