Sun Dec 8th through Sat the 14th, 2019 at Vancouver Convention Center
The paper is well-written and can be easily followed. I did not carefully check the proofs, but the results are reasonable and the methodology is correct. The results are mildly significant in my opinion.
This paper solves an open problem in the analysis of some variants of extragradient. On the positive side, I found the paper to be clear and well written. I particularly appreciated the review of single-call variants of extragradient in Section 3. I reviewed some key results that are proven in the appendix (Lemma 2), which seemed correct. On the negative side, I found their results on non-monotone operators (Theorem 4.) to be rather disappointing, since it only applies when the iterates are already in a neighborhood of the solution and the operator to be (basically) strongly monotone in that region. It is nothing more than a localized version of previous results. # Post rebuttal I read te autors rebuttal and the other reviewer's review. My score remains unchanged.
In this paper, the authors study the EG algorithm and its variants in the optimization of VI with single oracle. In the convergence analysis, a unified way is proposed. Then the ergodic and last-iterate convergences are discussed with monotone and non-monotone operators in both deterministic and stochastic cases. The authors mentioned their motivation clearly. Some related works were discussed in detail and the paper is well written.