Interpreting generative adversarial network (GAN) training as approximate divergence minimization has been theoretically insightful, spurred discussion, and lead to theoretically and practically interesting extensions such as f-GANs and Wasserstein GANs. In this paper we show that the widely used "non-saturating" training scheme can also be interpreted in this way, specifically as minimizing a particular reverse KL-like f-divergence. We also develop a number of theoretical tools to help compare and classify f-divergences. We hope these results may help to clarify some of the theoretical discussion surrounding the divergence minimization view of GAN training.
######## Updated Review #########
I would like to thank the author(s) for their rebuttal, which I have carefully read. I also appreciate the effort made to improve the paper. My overall evaluation of the paper stands unchanged. 
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#### My review is based on the updated paper downloaded from the anonymous link. ####
This paper discusses alternative training strategies for f-GANs. While the discussion has some interesting points, the presentation needs to be much improved. It is not easy to follow this paper in its current form, and the main results are not properly emphasized. As such, I am not certain of its real contribution. f-GANs are not routinely used in practice (except for the vanilla JSD and RKL), and as far as I can tell the saturating gradient issue is no longer a central concern (it has been well addressed years ago, with, e.g. WGANs). I am voting to reject this submission, but I am willing to re-evaluate this paper if the author(s) significantly improves their writing. 
- In Section 2, what does it mean by "the Fisher metric of the family"? The concept of Fisher metric is defined anywhere in the text, and there is no reference to it.
- It is not is intuitive why the second derivative of f_R takes the form $u^{-3} f''(u^{-1})$ (given above Eqn (2)). Please elaborate. 
- Please avoid the use of subjective phrases such as "imagining", "get a feel", etc. I am guessing the author(s) are trying to suggest taking a visual inspection of the discrepancies projected on the log-likelihood ratio axis (which is 1D) and figure out which f-div might be more appropriate. 
- Fig. 3 needs legends. There are two solid (dotted, resp) lines in the Figure, and I am guessing one of them is for the saturating and the other for the non-saturating gradient. This needs to be specified because the line specs are identical. 
- After going through the entire paper, I would highly recommend the author(s) to take a course in academic writing. The main contributions are not highlighted and some of the key concepts are not even properly defined. For example, analysis of the non-saturating gradient, which is supposedly the main result of this submission, appeared in pp. 7, by which time most readers have exhausted their patience. The vanilla version of the non-saturating scheme never appeared in the main text. The notation system is also non-standard, where the notation $\bar{\lambda}$, normally reserved for average/expectation, has been used to denote the gradient wrt $\lambda$. The writing can be very unprofessional at times, for example, "the answers to these questions are yes, yes and no respectively".  
- I do not know why the author(s) inserted one toy experiment in the paper, as it serves no purpose. Each model converges to their respectively optimal, as expected. There is no discussion of how to choose an appropriate f-div or (f,g) hybrid in practice. 
- I totally agree with the author(s) on the point that this is a note (sec 7, second paragraph), rather than an academic paper. There is a lot of derivations in the paper, but insightful discussions are limited in the sense that it is not clear how to connect these results to improve practice. The section titles also read like bullet points in a note. 
- Not certain about the significance of this paper. The derivations are fairly standard and I can not find any useful proposals that might benefit the practice of f-GAN training. There is a number of papers discussing non-saturating GAN training (see sec 8), and I do not think this paper adds too much value to this discussion.