Last-Iterate Convergence of Saddle-Point Optimizers via High-Resolution Differential Equations
Keywords:
Variational inequality, convergence, high resolution differential equations, saddle-point optimizers, continuous time methods.Abstract
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.
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