NeurIPS 2020

Optimistic Dual Extrapolation for Coherent Non-monotone Variational Inequalities

Meta Review

Originally, all reviewers recommended weak accept (6). This paper presents a single step version of Nesterov's dual extrapolation method (and a stochastic variant), with guarantees for coherent (nonmonotone) variational inequalities (see R2 Q1). The reviewers underlined the algorithmic contribution, as well as the interesting theoretical contribution of this work (though there is no empirical study of its performance). However, several concerns were expressed about the quality of the writing, especially the disconnect between the appendix and the main paper. The reviewers carefully considered the rebuttal and discussed the work. After the rebuttal, R4 decided to downgrade their score to weak reject (5), mainly because they thought the write-up needed a major revision. On the other hand, R2 in discussion argued that the paper should be accepted given its nice contributions, despite some issues with the presentation, and upgraded their rating to a 7.. They were hesitating between a 6 and 7 for their score, and thought that the authors could revise their paper fine for the camera ready version to address the reviewers concerns. All reviewers agreed in discussion that the paper made nice algorithmic and theoretical contribution. The AC also considered that this paper seems to be a significant improvement over its ICML submission, where it was already close to be accepted. The authors improved the novelty of the work and the theoretical contributions by proposing a single step version of the algorithm (instead of the traditional two steps like in their ICML submission), yielding novel proof techniques. Given the above, the AC agrees with R2 and does not think another round of reviewing is necessary for this paper, and recommends acceptance. The authors should carefully consider the reviews and implement the asked changes in the camera ready version. Among others, the title change from R2; important clarifications from all reviewers; adding the simulation results as proposed by R2; and careful re-writing of appendix to be consistent with main paper.