Paper:
Generative Adversarial Networks (GANs) are powerful framework for modeling complex and high dimensional data. The training of GANs is difficult because the optimization is a min-max problem. This paper understands GANs from the perspective of duality gap and shows that the duality gap can be a good metric to evolution the difference between the true data distribution and the distribution generated by generator. Training GANs using the duality gap can provide competitive results. Furthermore, we establish the generalization error bound of the duality gap to help design the neural network architecture and select the sample size.

Review:
This paper has problems with clarity/polish and experimental design that are sufficiently severe
to merit rejection by themselves.
Regarding clarity/polish:
I am generally not super picky about these things, but there does have to be some standard.
This paper looks very hastily put together, especially pages 7 and 8.
There are many typos and unclear statements.
Just a few examples:
> Generative Adversarial Networks (GANs) are powerful framework for (in the abstract)
> be a good metric to evolution the difference (in the abstract)
> In the past few years, Generative Adversarial Networks (GANs) (Goodfellow et al., 2014) are impactful because it has shown lots of great results for many AI tasks, (first sentence)
> It means that there is no an unanimous metric to represent the difference between the true data distribution and the generated distribution
What does this mean? People have mostly settled on using FID for this.
 
> It is also difficult to know whether the generated distribution is close to the true distribution, and this is often observed by human eyes.
Isn't this just restating the point made in the first sentence?
Regardless, nobody really uses human evaluation anymore - so this is just not correct.
>  It means that if the original generator and discriminator are random, it is difficult to confirm that the generator and discriminator can converge to the ideal conclusion by training with given data.
But this paper doesn't propose a way to solve that problem, so it's strange to mention this here in this way.
These issues would maybe be excusable if not for the totally inadequate experimental validation.
A non-exhaustive list of methodological problems with the (single) experiment:
1. The experiment uses a single run each of the baseline and DG-GAN, when it's well-known that GAN training runs
have inter-run variance larger than the difference in score reported in Fig 1 and 2.
2. The models have not been trained for long enough.
3. The architecture of the neural networks used for the Generator and Discriminator is very non-standard, which
probably leads to:
4. The scores achieved by the baseline are very far from state of the art, making the comparison mostly useless,
and rendering the third claim from the introduction ("We propose an new algorithm with the new metric which demonstrates better results than state-of-the-art algorithms.") completely untrue.
In light of these other issues, I haven't checked the proofs.