Venue: ICLR 2018 conference

Reviews:

final_score: rating: 5: Marginally below acceptance threshold
review_content: The paper applies tools from online learning to GANs. In the case of a shallow discriminator, the authors proved some results on the convergence of their proposed algorithm (an adaptation of FTRL) in GAN games, by leveraging the fact that when D update is small, the problem setup meets the ideal conditions for no-regret algorithms. The paper then takes the intuition from the semi-shallow case and propose a heuristic training procedure for deep GAN game. 

Overall the paper is very well written. The theory is significant to the GAN literature, probably less so to the online learning community. In practice, with deep D, trained by single gradient update steps for G and D, instead of the "argmin" in Algo 1., the assumptions of the theory break. This is OK as long as sufficient experiment results verify that the intuitions suggested by the theory still qualitatively hold true. However, this is where I have issues with the work:

1) In all quantitative results, Chekhov GAN do not significantly beat unrolled GAN. Unrolled GAN looks at historical D's through unrolled optimization, but not the history of G. So this lack of significant difference in results raise the question of whether any improvement of Chekhov GAN is coming from the online learning perspective for D and G, or simply due to the fact that it considers historical D models (which could be motivated by sth other than the online learning theory).

2) The mixture GAN approach suggested in Arora et al. (2017) is very related to this work, as acknowledged in Sec. 2.1, but no in-depth analysis is carried out. I suggest the authors to either discuss why Chekhov GAN is obviously superior and hence no experiments are needed, or compare them experimentally. 

3) In the current state, it is hard to place the quantitative results in context with other common methods in the recent literature such as WGAN with gradient penalty. I suggest the authors to either report some results in terms of inception scores on cifar10 with similar architectures used in other methods for comparison. Alternatively please show WGAN-GP and/or other method results in at least one or two experiments using the evaluation methods in the paper. 

In summary, almost all the experiments in the paper are trying to establish improvement over basic GAN, which would be OK if the gap between theory and practice is small. But in this case, it is not. So it is not entirely convincing that the practical Algo 2 works better for the reason suggested by the theory, nor it drastically improves practical results that it could become the standard technique in the literature. 
review_title: Good theory, but large gap with the practical proposal is not sufficiently bridged by experimental evidence

final_score: rating: 8: Top 50% of accepted papers, clear accept
review_content: This is an interesting paper, exploring GAN dynamics using ideas from online learning, in particular the pioneering "sparring" follow-the-regularized leader analysis of Freund and Schapire (using what is listed here as Lemma 4). By restricting the discriminator to be a single layer, the maximum player plays over a concave (parameter) space which stabilizes the full sequence of losses so that Lemma 3 can be proved, allowing proof of the dynamics' convergence to a Nash equilibrium. The analysis suggests a practical (heuristic) algorithm incorporating two features which emerge from the theory: L2 regularization and keeping a history of past models. A very simple queue for the latter is shown to do quite competitively in practice.

This paper merits acceptance on theoretical merits alone, because the FTRL analysis for convex-concave games is a very robust tool from theory (see also the more recent sequel [Syrgkanis et al. 2016 "Fast convergence of regularized learning in games"]) that is natural to employ to gain insight on the much more brittle GAN case. The practical aspects are also interesting, because the incorporation of added randomness into the mixed generation strategy is an area where theoretical justifications do motivate practical performance gains; these ideas could clearly be developed in future work.
review_title: Powerful theory tools applied naturally to GAN dynamics

final_score: rating: 7: Good paper, accept
review_content: It is well known that the original GAN (Goodfellow et al.) suffers from instability and mode collapsing. Indeed, existing work has pointed out that the standard GAN training process may not converge if we insist on obtaining pure strategies (for the minmax game). The present paper proposes to obtain mixed strategy through an online learning approach. Online learning (no regret) algorithms have been used in finding an equilibrium for zero sum game. However, most theoretical convergence results are known for convex-concave loss. One interesting theoretical contribution of the paper is to show that convergence result can be proved if one player is a shallow network (and concave in M).In particular, the concave player plays the FTRL algorithm with standard L2 regularization term. The regret of concave player can be bounded using existing result for FTRL. The regret for the other player is more interesting: it uses the fact the adversary's strategy doesn't change too drastically. Then a lemma by Kalai and Vempala can be used. The theory part of the paper is reasonable and quite well written. 

Based on the theory developed, the paper presents a practical algorithm. Compared to the standard GAN training, the new algorithm returns mixed strategy and examine several previous models (instead of the latest) in each iteration. The paper claims that this may help to prevent model collapsing.

However, the experimental part is less satisfying. From figure 2, I don't see much advantage of Checkhov GAN. In other experiments, I don't see much improvement neither (CIFAR10 and CELEBA).The paper didn't really compare other popular GAN models, especially WGAN and its improved version, which is already quite popular by now and should be compared with.

Overall, I think it is a borderline paper.

-------------------------
I read the response and the new experimental results regarding WGAN.
The experimental results make more sense now.
It would be interesting to see whether the idea can be applied to more recent GAN models and still perform better.
I raised my score to 7.


review_title: borderline paper

Meta-review: This paper presents a GAN training algorithm motivated by online learning. The method is shown to converge to a mixed Nash equilibrium in the case of a shallow discriminator. In the initial version of the paper, reviewers had concerns about weak baselines in the experiments, but the updated version includes comparisons against a variety of modern GAN architectures which have been claimed to fix mode dropping. This seems to address the main criticism of the reviewers. Overall, this paper seems like a worthwhile addition to the GAN literature.
Decision: Accept (Poster)