Geodesic
Last-iterate convergence of saddle-point optimizers via high-resolution differential equations
Minimax theory and its applications, Tome 8 (2023) no. 2
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Several widely-used first-order saddle-point optimization methods yield an identical continuous time ordinary differential equation (ODE) that is identical to that of the Gradient Descent Ascent (GDA) method when derived naively. However, the convergence properties of these methods are qualitatively different, even on simple bilinear games. Thus the ODE perspective, which has proved powerful in analyzing single-objective optimization methods, has not played a similar role in saddle-point optimization.
Mots-clés : Variational inequality, convergence, high resolution differential equations, saddle-point optimizers, continuous time methods 
@article{MTA_2023_8_2_a4,
     author = {Tatjana Chavdarova and Michael I. Jordan and Manolis Zampetakis},
     title = {Last-iterate convergence of saddle-point optimizers via high-resolution differential equations},
     journal = {Minimax theory and its applications},
     year = {2023},
     volume = {8},
     number = {2},
     zbl = {1557.65121},
     url = {http://geodesic.mathdoc.fr/item/MTA_2023_8_2_a4/}
}
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Tatjana Chavdarova; Michael I. Jordan; Manolis Zampetakis. Last-iterate convergence of saddle-point optimizers via high-resolution differential equations. Minimax theory and its applications, Tome 8 (2023) no. 2. http://geodesic.mathdoc.fr/item/MTA_2023_8_2_a4/