Two-timescale Extragradient for Finding Local Minimax Points

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Chae, Jiseok, Kim, Kyuwon, Kim, Donghwan
Format: Preprint
Published: 2023
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911846948143104
author Chae, Jiseok
Kim, Kyuwon
Kim, Donghwan
author_facet Chae, Jiseok
Kim, Kyuwon
Kim, Donghwan
contents Minimax problems are notoriously challenging to optimize. However, we present that the two-timescale extragradient method can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the second-order necessary condition of local minimax points, under mild conditions that the two-timescale gradient descent ascent fails to work. This work provably improves upon all previous results on finding local minimax points, by eliminating a crucial assumption that the Hessian with respect to the maximization variable is nondegenerate.
format Preprint
id arxiv_https___arxiv_org_abs_2305_16242
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Two-timescale Extragradient for Finding Local Minimax Points
Chae, Jiseok
Kim, Kyuwon
Kim, Donghwan
Optimization and Control
Machine Learning
Minimax problems are notoriously challenging to optimize. However, we present that the two-timescale extragradient method can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the second-order necessary condition of local minimax points, under mild conditions that the two-timescale gradient descent ascent fails to work. This work provably improves upon all previous results on finding local minimax points, by eliminating a crucial assumption that the Hessian with respect to the maximization variable is nondegenerate.
title Two-timescale Extragradient for Finding Local Minimax Points
topic Optimization and Control
Machine Learning
url https://arxiv.org/abs/2305.16242