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In this paper we consider solving saddle point problems using two variants ofGradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic GradientDescent Ascent (OGDA) methods. We show that both of these algorithms admit aunified analysis as approximations of the classical proximal point method forsolving saddle point problems. This viewpoint enables us to develop a newframework for analyzing EG and OGDA for bilinear and strongly convex-stronglyconcave settings. Moreover, we use the proximal point approximationinterpretation to generalize the results for OGDA for a wide range ofparameters.

A Unified Analysis of Extra-gradient and Optimistic Gradient Methods for Saddle Point Problems: Proximal Point Approach