Evolutionary Strategies (ES) are a popular family of black-box zeroth-order optimization algorithms which rely on search distributions to efficiently optimize a large variety of objective functions. This paper investigates the potential benefits of using highly flexible search distributions in ES algorithms, in contrast to standard ones (typically Gaussians). We model such distributions with Generative Neural Networks (GNNs) and introduce a new ES algorithm that leverages their expressiveness to accelerate the stochastic search. Because it acts as a plug-in, our approach allows to augment virtually any standard ES algorithm with flexible search distributions. We demonstrate the empirical advantages of this method on a diversity of objective functions.
Summary:
As the title of the paper states, this paper tries to improve evolution strategies (ES) using a generative neural network. In the standard ES candidate solution is generated from a multivariate normal distribution, where the parameters of the distribution are adapted during the optimization process. The authors claim that the gaussian distribution, i.e., the ellipsoidal shape of the sampling distribution, is not adequate for the objective functions such as multimodal functions or functions with curved ridge levelsets such as the well-known Rosenbrock functions. The motivation is clearly stated. The technique is interesting and non-trivial. However, the experimental results are not very convincing to conclude that the proposed approach achieves the stated goal. Moreover, this paper may fit more to optimization conferences such as GECCO. 
Because of the empirical results, I would rate this paper as the border line (around 5), but due to the slightly annoying rating system the rate appears as 6. 
Comments:
P2: "Efficient Natural Evolutionary Strategies (xNES) (Sun et al., 2009) has been shown to reach state- of-the-art performances on a large ES benchmark." 
This algorithm is "eNES" and  this algorithm is not competitive with the state-of-the-art ES such as CMA-ES. The authors might want to refer to exponential NES, which is xNES, proposed by Glasmachers et al 2010.
P5: "Indeed, other bijective GNN models like the Real-NVP (Dinh et al., 2016) introduce non-volume preserving transformations, which can easily overfit and lead to premature concentration and convergence." Has it been reported in a reference? If so provide the reference. If not, the authors should state that it has been observed the authors preliminary study. In any case, I think it depends how the model is used or trained, and this statement itself is not universally true.
P7: "By using fη instead of gη as the push-forward map of the NICE model, we ensure that the flexibility brought by the GNN only impacts the tails of the search distribution. As detailed in an ablation study presented in Appendix F, this additional tool turns out to be essential in order to use GNNs for ES."
I barely understood this point. Please make is clearer.
P8: Experimental results are not very convincing. The experiments are limited to dimension 2, 5, 10 and only a few functions are selected from the BBOB test function suite. How about on 20D? What happens if the target is 1e-8, which is the default setting in BBOB? 
Figure 3 looks interesting, and this is what the authors are trying to achieve. Therefore, it looks like the authors reached the stated objective. However, this is only 2D. No results are provided to convince that the proposed strategy achieved the stated objective. 
Figure 4  simply looks that the proposed algorithm failed to reach the "flexibility" stated in Section 2: "Another limitation of classical search distribution is their inability to follow multiple hypothesis, that is to explore at the same time different local minima. Even if mixture models can show such flexibility, hyper-parameters like the number of mixtures have optimal values that are impossible to guess a priori."
From these results, I am not convinced that the proposed strategy really achieved more flexible distribution than the classical methods, and whether the flexibility contributes to improve the performance. 
Another critical point to be discussed is its usefulness. Since this algorithm is proposed to "improve evolution strategy" as a black-box optimizer (not for specific tasks), I expect to improve the state-of-the-art performance. Are the reported results outperform the CMA-ES? Based on Glasmachers et al (2010), xNES tends to require more objective function evaluations than CMA-ES, especially for higher dimensional cases. I am curious to know if the proposed approach outperforms the CMA-ES on Rosenbrock functions.