The limit points of (optimistic) gradient descent in min-max optimization
Name
NeurIPS-2018-the-limit-points-of-optimistic-gradient-descent-in-min-max-optimization-Paper.pdf
Description
Published version
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806.65 KB
Format
Adobe PDF
Checksum (MD5)
8a60a8b691f03f5f36ad123618d726ad
Author(s)
Daskalakis, C
Panageas, I
Date Issued
January 1, 2018
Journal
Advances in Neural Information Processing Systems
Citation
Daskalakis, C and Panageas, I. 2018. "The limit points of (optimistic) gradient descent in min-max optimization." Advances in Neural Information Processing Systems, 2018-December.
Version
Final published version
Abstract
© 2018 Curran Associates Inc.All rights reserved. Motivated by applications in Optimization, Game Theory, and the training of Generative Adversarial Networks, the convergence properties of first order methods in min-max problems have received extensive study. It has been recognized that they may cycle, and there is no good understanding of their limit points when they do not. When they converge, do they converge to local min-max solutions? We characterize the limit points of two basic first order methods, namely Gradient Descent/Ascent (GDA) and Optimistic Gradient Descent Ascent (OGDA). We show that both dynamics avoid unstable critical points for almost all initializations. Moreover, for small step sizes and under mild assumptions, the set of OGDA-stable critical points is a superset of GDA-stable critical points, which is a superset of local min-max solutions (strict in some cases). The connecting thread is that the behavior of these dynamics can be studied from a dynamical systems perspective.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://papers.nips.cc/paper/2018/hash/139c3c1b7ca46a9d4fd6d163d98af635-Abstract.html
