Title: A Unified Analysis of Extra-gradient and Optimistic Gradient Methods for Saddle Point Problems: Proximal Point Approach,
Abstract: We consider solving convex-concave saddle point problems. We focus on two
variants of gradient decent-ascent algorithms, Extra-gradient (EG) and
Optimistic Gradient (OGDA) methods, and show that they admit a unified analysis
as approximations of the classical proximal point method for solving
saddle-point problems. This viewpoint enables us to generalize EG (in terms of
extrapolation steps) and OGDA (in terms of parameters) and obtain new
convergence rate results for these algorithms for the bilinear case as well as
the strongly convex-concave case.