Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max
  Optimization   Motivated by applications in Game Theory, Optimization, and Generative
Adversarial Networks, recent work of Daskalakis et al \cite{DISZ17} and
follow-up work of Liang and Stokes \cite{LiangS18} have established that a
variant of the widely used Gradient Descent/Ascent procedure, called
"Optimistic Gradient Descent/Ascent (OGDA)", exhibits last-iterate convergence
to saddle points in {\em unconstrained} convex-concave min-max optimization
problems. We show that the same holds true in the more general problem of {\em
constrained} min-max optimization under a variant of the no-regret
Multiplicative-Weights-Update method called "Optimistic Multiplicative-Weights
Update (OMWU)". This answers an open question of Syrgkanis et al \cite{SALS15}.
  The proof of our result requires fundamentally different techniques from
those that exist in no-regret learning literature and the aforementioned
papers. We show that OMWU monotonically improves the Kullback-Leibler
divergence of the current iterate to the (appropriately normalized) min-max
solution until it enters a neighborhood of the solution. Inside that
neighborhood we show that OMWU is locally (asymptotically) stable converging to
the exact solution. We believe that our techniques will be useful in the
analysis of the last iterate of other learning algorithms.

11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ