Originality: I find the approach original and interesting, I find that other works have been cited and the section of related work is written clearly and detailed, it gives a nice overview. I think only that it is important to highlight more clearly the differences between [40] and the current work. In particular, it is unclear what is the penalty parameter, and how their method of adversarial training relates to this work - do they optimize a different bound or what quantities do they optimize, and do these quantities show up in the proposed bound? Quality: the work seems complete, and sound for as far as I could check. I could not check all the proofs in detail but I read the work in great detail.

Additional Feedback: Post-rebuttal comments: I've read the rebuttal and other reviews. The authors have addressed most of my concerns and hence I increase my score. I hope the authors would make the suggested edits in the revised version and explain the role of their main assumption. Can you explain why things fail if this assumption does not hold? Can you make use of a prior (in the case it is informative)?

All reviewers agree that the paper considers a problem of relevance (bandits with many arms) and shows interesting results about simple-to-implement learning algorithms based on the greedy principle. However, one lingering concern that arose during the discussions among the reviewers was whether/how the results obtained in the paper applied for the case when the number of arms is larger than the time horizon of the game (k T). It appears that the author response to this question has not been substantial. Though I can see that this will not be an issue -- the proof of Lemma 2 bounds regret with respect to the best possible reward of 1, the author(s) is/are requested to add a precise clarification of this regime in the updated version.

After rebuttal: The discussion of the method applicability in the rebuttal is convinced for me. I upgrade my score to 7. This paper proposes a learning-based approach for combinatorial optimization problems. Starting from an initial complete solution of the problem, several local rewriting updates are applied to the solution iteratively. In each rewriting step, a local region and an updating rule are picked to update the solution and two networks are trained by reinforcement learning to pick local regions and updating rules.

The reviewers liked the paper and were further convinced by the response. Please take their suggestions into account when preparing the final version of your paper.

This work is original in its use of deep reinforcement learning and graph neural networks to learn novel search control heuristics for SAT solving. While the techniques used are not novel themselves, the application domain is. The authors do a good job of surveying related work in this area and situating their contributions in this landscape. The paper is well-written and I found it very easy to follow the details of the proposed approach and the authors' results. Technically, the work presented is solid, though I have a few comments/suggestions here.

The reviewers were positive about this paper based upon their initial read. The authors response addressed their concerns, so they were even more comfortable with a positive outcome after the author response. I encourage the authors to incorporate their responses to the reviewer concerns into any final version of the paper.

Weaknesses: Though there are some merits of the paper, here are a bunch of major problems of the submission: 1. PL condition is a very strong assumption. Although it does not require convexity-concavity, it is a global condition, which roughly requires similar properties of strong convexity-concavity. I agree there are some applications of min-max problems under PL condition, as mentioned in the paper, but the applications are extremely limited, and I am not sure they are important applications to ML community. In general, nonconvex-nonconcave min-max problems won't satisfy PL condition. To this extend, the title of the paper is a bit misleading, and it should mention PL condition explicitly.

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.

This paper aims at solving the saddle point problem \min_{x} \max_{y} g(x, y) where g(x, \cdot) is concave for each x and g(\cdot, y) is either strongly convex or nonconvex for every y . The authors introduce a new algorithm called DIAG which combines Mirror-prox and Nesterov's AGD to solve the minimax problem. For the case that g is strongly-convex with respect to x, the authors show that DIAG has a convergence rate of \mathcal{O}(1/k 2) when the suboptimality for a pair of point (\hat{x},\hat{y}) is defined as the primal-dual optimality gap \max_{y} g(\hat{x},y) - \min_{x} g(x, \hat{y}) . For the case that g is nonconvex with respect to x, the authors show that DIAG finds an \epsilon -first-order stationary point (FOSP) after at most \mathcal{O}(1/\epsilon 3) gradient evaluations. The convergence criteria considered in this paper for solving a strongly convex-concave problem is interesting.