Min-Max Optimization Made Simple: Approximating the Proximal Point Method via Contraction Maps

Volkan Cevher, Georgios Piliouras, Ryann Sim, Stratis Skoulakis

Abstract: In this paper we present a first-order method that admits near-optimal convergence rates for convex/concave min-max problems while requiring a simple and intuitive analysis. Similarly to the seminal work of Nemirovski [26] and the recent approach of Piliouras et al. [28] in normal form games, our work is based on the fact that the update rule of the Proximal Point method (PP) can be approximated up to accuracy ε with only O (log 1/ε) additional gradient-calls through the iterations of a contraction map. Then combining the analysis of (PP) method with an error-propagation analysis we establish that the resulting first order method, called Clairvoyant Extra Gradient, admits near-optimal time-average convergence for general domains and last-iterate convergence in the unconstrained case.