Our bound achieves linear convergence rate and tighter dependency on condition numbers, especially when $L_{\x\y}\ll L$ (i.e., the weak interaction regime). Via simple reduction, our new bound also implies improved bounds for strongly convex-concave problems and convex-concave problems.

Relation to Prior Work: In addition to the papers mentioned above, the relation to the literature of monotone VI should be discussed in details. The convex-concave min-max falls into the category of monotone VIs and there are many works in the literature addressing that. For example, the following papers should be discussed: Ronald E Bruck Jr. Dual extrapolation and its applications to solving variational inequalities and related problems. Solving variational inequalities with monotone operators on domains given by linear minimization oracles.

Authors propose a novel algorithm that achieves linear convergence rate and improved dependence on the condition numbers, compared to prior work.

Our bound achieves linear convergence rate and tighter dependency on condition numbers, especially when L_{\x\y}\ll L (i.e., the weak interaction regime). Via simple reduction, our new bound also implies improved bounds for strongly convex-concave problems and convex-concave problems.