Paper:
Reinforcement learning algorithms, though successful, tend to over-fit to training environments, thereby hampering their application to the real-world. This paper proposes WR 2 L -a robust reinforcement learning algorithm with significant robust performance on low and high-dimensional control tasks. Our method formalises robust reinforcement learning as a max-min game with a constraint derived from Wasserstein distance, and we propose an efficient and scalable algorithm to solve it. Our algorithm applies zero-order optimisation method that we believe can be useful to numerical optimisation in general. Apart from the formulation, we also propose an efficient and scalable solver following a novel zero-order optimisation method that we believe can be useful to numerical optimisation in general. We empirically demonstrate significant gains compared to standard and robust state-of-the-art algorithms on high-dimensional MuJuCo environments.

Review:
The paper proposes a novel solution to a *restricted* reinforcement learning problem. I am not quite sure if I understand the restriction from the text or thus what relevance this has in applications. The method factorizes the transition dynamics (where they rely on a parametrized solver) and a policy modeled by a NN and trained with policy gradient with monte-carlo returns. The ultimate goal is robust control so they care about the maximin objective of highest return along the worst trajectory. The robustness is implemented as a constraint in the dynamics optimization: a wasserstein distance between the distribution of samples obtained applying the learnt policy and learnt dynamics parameters and those obtained by random policy and some reference dynamics model. They solve the maximin by alternating minimization on the dynamics and policy. The contribution is in the intricacies of computing the wasserstein efficiently in particular they obtain a perturbation based estimate of the gradient of the dynamics parameters. The experiments seem sensible but I  have some suggestions for improvement.
I have published in RL but my familiarity with Wasserstein and robustness is limited. I have not checked the derivations in the appendix in detail. If there is a high score I'll have a closer look. 
Major points:
1) The restriction imposed is that only part of the transition model is really learnt. So it is more like a system identification setup ?! Why is that necessary ? 
2) The explanation in on page 4 about how the wasserstein distance is computed is a bit unclear. Is it sampling data from the P_\phi and \pi on one hand and P_0 and \pi_{Uniform} ? Then there is a bucketing step (what does it mean ? how is it computed ?). Is it then a discrete wasserstein between the two empirical distributions ?! What is Monte-Carlo in this case ?
3) All the approximations done in the method should be more clearly explained because they are relevant both to people who might apply the method in practice as well as other researchers that might want to build on/ improve on it.
4) The experiments seem interesting but I am not sure how to interpret the results. If a method has access to a simulator and a representation of the relevant dynamics parameter space it seems clear that it will be more robust. This is impressive if one has a simulator and can infer some state components e.g. in pendulum starting with an empty simulator and adding a pendulum. But that seems as hard or maybe even harder than trying to learn an implicit transition model just from observations. 
5) Imagine the method only gets observations and an imperfect simulator, which will be the case in an application, what are the caveats we should have in mind ?
6) Can you have a learnt model baseline and compare your learnt and simulation ? Maybe it would have to be a latent variable model so you can do the same inference for internal parameters and still do an adaptation in the same way as now. This seems easy since it is a supervised problem.