Last iterate convergence in no-regret learning: constrained min-max optimization for convex-concave landscapes
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
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2020
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| _version_ | 1866914059218059264 |
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| author | Lei, Qi Nagarajan, Sai Ganesh Panageas, Ioannis Wang, Xiao |
| author_facet | Lei, Qi Nagarajan, Sai Ganesh Panageas, Ioannis Wang, Xiao |
| contents | In a recent series of papers it has been established that variants of Gradient Descent/Ascent and Mirror Descent exhibit last iterate convergence in convex-concave zero-sum games. Specifically, \cite{DISZ17, LiangS18} show last iterate convergence of the so called "Optimistic Gradient Descent/Ascent" for the case of \textit{unconstrained} min-max optimization. Moreover, in \cite{Metal} the authors show that Mirror Descent with an extra gradient step displays last iterate convergence for convex-concave problems (both constrained and unconstrained), though their algorithm does not follow the online learning framework; it uses extra information rather than \textit{only} the history to compute the next iteration. In this work, we show that "Optimistic Multiplicative-Weights Update (OMWU)" which follows the no-regret online learning framework, exhibits last iterate convergence locally for convex-concave games, generalizing the results of \cite{DP19} where last iterate convergence of OMWU was shown only for the \textit{bilinear case}. We complement our results with experiments that indicate fast convergence of the method. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2002_06768 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Last iterate convergence in no-regret learning: constrained min-max optimization for convex-concave landscapes Lei, Qi Nagarajan, Sai Ganesh Panageas, Ioannis Wang, Xiao Machine Learning Computer Science and Game Theory In a recent series of papers it has been established that variants of Gradient Descent/Ascent and Mirror Descent exhibit last iterate convergence in convex-concave zero-sum games. Specifically, \cite{DISZ17, LiangS18} show last iterate convergence of the so called "Optimistic Gradient Descent/Ascent" for the case of \textit{unconstrained} min-max optimization. Moreover, in \cite{Metal} the authors show that Mirror Descent with an extra gradient step displays last iterate convergence for convex-concave problems (both constrained and unconstrained), though their algorithm does not follow the online learning framework; it uses extra information rather than \textit{only} the history to compute the next iteration. In this work, we show that "Optimistic Multiplicative-Weights Update (OMWU)" which follows the no-regret online learning framework, exhibits last iterate convergence locally for convex-concave games, generalizing the results of \cite{DP19} where last iterate convergence of OMWU was shown only for the \textit{bilinear case}. We complement our results with experiments that indicate fast convergence of the method. |
| title | Last iterate convergence in no-regret learning: constrained min-max optimization for convex-concave landscapes |
| topic | Machine Learning Computer Science and Game Theory |
| url | https://arxiv.org/abs/2002.06768 |