Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Last iterate convergence in no-regret learning: constrained min-max
  optimization for convex-concave landscapes   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.

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The categories of this paper are: mtrl-th
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The categories of this paper are: math
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int