当前位置: X-MOL 学术arXiv.cs.GT › 论文详情
On the convergence of single-call stochastic extra-gradient methods
arXiv - CS - Computer Science and Game Theory Pub Date : 2019-08-22 , DOI: arxiv-1908.08465
Yu-Guan Hsieh; Franck Iutzeler; Jérôme Malick; Panayotis Mertikopoulos

Variational inequalities have recently attracted considerable interest in machine learning as a flexible paradigm for models that go beyond ordinary loss function minimization (such as generative adversarial networks and related deep learning systems). In this setting, the optimal $\mathcal{O}(1/t)$ convergence rate for solving smooth monotone variational inequalities is achieved by the Extra-Gradient (EG) algorithm and its variants. Aiming to alleviate the cost of an extra gradient step per iteration (which can become quite substantial in deep learning applications), several algorithms have been proposed as surrogates to Extra-Gradient with a \emph{single} oracle call per iteration. In this paper, we develop a synthetic view of such algorithms, and we complement the existing literature by showing that they retain a $\mathcal{O}(1/t)$ ergodic convergence rate in smooth, deterministic problems. Subsequently, beyond the monotone deterministic case, we also show that the last iterate of single-call, \emph{stochastic} extra-gradient methods still enjoys a $\mathcal{O}(1/t)$ local convergence rate to solutions of \emph{non-monotone} variational inequalities that satisfy a second-order sufficient condition.
更新日期:2020-02-12

 

全部期刊列表>>
物理学研究前沿热点精选期刊推荐
chemistry
《自然》编辑与您分享如何成为优质审稿人-信息流
欢迎报名注册2020量子在线大会
化学领域亟待解决的问题
材料学研究精选新
GIANT
自然职场线上招聘会
ACS ES&T Engineering
ACS ES&T Water
ACS Publications填问卷
屿渡论文,编辑服务
阿拉丁试剂right
南昌大学
王辉
南方科技大学
刘天飞
隐藏1h前已浏览文章
课题组网站
新版X-MOL期刊搜索和高级搜索功能介绍
ACS材料视界
天合科研
x-mol收录
X-MOL
苏州大学
廖矿标
深圳湾
试剂库存
down
wechat
bug