Robust Imitation of Diverse Behaviors
Deep generative models have recently shown great promise in imitation learning for motor control. Given enough data, even supervised approaches can do one-shot imitation learning; however, they are vulnerable to cascading failures when the agent trajectory diverges from the demonstrations. Compared to purely supervised methods, Generative Adversarial Imitation Learning (GAIL) can learn more robust controllers from fewer demonstrations, but is inherently mode-seeking and more difficult to train. In this paper, we show how to combine the favourable aspects of these two approaches. The base of our model is a new type of variational autoencoder on demonstration trajectories that learns semantic policy embeddings. We show that these embeddings can be learned on a 9 DoF Jaco robot arm in reaching tasks, and then smoothly interpolated with a resulting smooth interpolation of reaching behavior. Leveraging these policy representations, we develop a new version of GAIL that (1) is much more robust than the purely-supervised controller, especially with few demonstrations, and (2) avoids mode collapse, capturing many diverse behaviors when GAIL on its own does not. We demonstrate our approach on learning diverse gaits from demonstration on a 2D biped and a 62 DoF 3D humanoid in the MuJoCo physics environment.
This work deals with the problem of modeling joint action/state trajectory spaces of dynamical systems using a supervised imitation learning paradigm.  It approaches the problem by defining a Variational Autoencoder (VAE) that maps the state sequence, via a latent representation, into a (state,action) pair.  
The approach is validated on three articulated body controller modeling problems: a robotic arm, a 2D biped, and a 3D human body motion modeling.
Prior work: the work closely follows (extends) the approach of Generative Adversarial Imitation Learning [11].  The difference here is that, through the use of VAE, the authors claim to have avoided the pitfall of GAN know as mode collapsing.
Summary
+ Addresses a challenging problem of learning complex dynamics controllers / control policies
+ Well-written introduction / motivation
+ Appealing qualitative results on the three evaluation problems. Interesting experiments with motion transitioning.  
- Modeling formulation is somewhat different from GAIL (latent representation) but it rather closely follows GAIL
- Many key details are omitted (either on purpose, placed in appendix, or simply absent, like the lack of definitions of terms in the modeling section, details of the planner model, simulation process, or the details of experimental settings)
- Experimental evaluation is largely subjective (videos of robotic arm/biped/3D human motion)
- Paper appears written in haste or rewritten from a SIGGRAPH like submission 
- Relies significantly on work presented in an anonymous NIPS submission
Detailed comments
In general, I like the focus of this paper; designing complex controllers for dynamic systems is an extremely challenging task and the approach proposed here looks reasonable.  The use of the VAE is justified and the results, subjectively, are appealing.
However, so many details are missing here and some parts of the discussion are unclear or not justified, in my view.
For instance, the whole modeling section (3), while not so obscure, still ends up not defining many terms.  Eg, what is \pi_E in the first eq of 3.2? (Not numbered, btw) What is \theta in eq3? (also used elsewhere) .  What are all the weight terms in the policy model, end of sec 3 (not numbered)?  You say you initialize theta to alpha wights, but what does that mean?
What is the purpose of Lemma 1?  The whole statement following it, l 135-145 sound unclear and contradictory.  Eg, you say that eq5 avoids the problem of collapse, yet you state in those lines that is also has the same problem?
The decoder models for (x,a) are not explicitly defined.
How is the trajectory simulation process actually accomplished?  This is somewhat tersely described in l168-172.
How are transitions between categories of different motion types modeled as you do not explicitly encode the category class?  It is obviously done in the z-space, but is it some linear interpolation?  It appears to be (l174-176) but is it timed or instantaneous?
What are all the numbers in the Action Decoder Sizes column of Tab 1, appendix?