Review for NeurIPS paper: Global Convergence and Variance Reduction for a Class of Nonconvex-Nonconcave Minimax Problems

This paper studies AGDA/Stoc-AGDA for minimax problems that may not be nonconvex-nonconcave but obey the two-sides Polyak-Łojasiewicz (PL), Moreover, this paper proposes a variance reduction version of AGDA and achieves better complexity results. The reviewers thought the problem setting was interesting and relevant to Neurips but also had a variety of concerns. These concerns were partially mitigated based on the response but other concerns remained. The reviewers had a spirited and comprehensive technical discussion about the merits of this paper. Two reviewers raised their score R4 - 4-5 and R2 4- 7 while one reviewer slightly lowered their score 8- 7. Based on the reviews, response, discussion and my own reading the main pros and cons of this paper are as follows.