Paper:
Many approaches to hierarchical reinforcement learning aim to identify sub-goal structure in tasks. We consider an alternative perspective based on identifying behavioral 'motifs'-repeated action sequences that can be compressed to yield a compact code of action trajectories. We present a method for iteratively compressing action trajectories to learn nested behavioral hierarchies of arbitrary depth, with actions of arbitrary length. The learned temporally extended actions provide new action primitives that can participate in deeper hierarchies as the agent learns. We demonstrate the relevance of this approach for tasks with non-trivial hierarchical structure and show that the approach can be used to accelerate learning in recursively more complex tasks through transfer.

Review:
The paper proposes a method that aims at encoding trajectories (described as a sequence of actions) into a set of discrete codes with a hierarchical structure. The principle of the algorithm (as far as the article allows me to understand) is to apply multiple iterations of classical sparse coding over the trajectories. The experimental section on simple (deterministic) tasks shows that the SSC method is able to extract interesting options, which can then be used to learn faster on some close domains.
In terms of positioning, I find the idea of the paper interesting (i.e encoding trajectories through discrete symbols) since it uses sparse coding approaches which, as far as I know, are not classical in the RL domain. This type of approach can give us both a meaningful insight about the "nature" of the learned policy (as it is the case in the paper that compresses expert trajectories), and can also become a manner to constraint an RL algorithm to force it to exhibit behaviors that could seem more natural to humans.  
But the way it is done in this article is disappointing. First of all, the article is badly written, and I am still not sure to fully understand how the algorithm exactly works. Indeed, many notations are not well defined (see at the end of the review), and it makes the algorithm 1 difficult to catch. Then, the authors consider that trajectories are represented as sequences of actions (using one-hot encoding) and do not discuss this hard choice: representing trajectories as a sequence of actions usually rely on the assumption that both the environment is deterministic, and the initial state is always the same. Is it the case in this paper? If it is, it clearly restricts the applicability of the technique. If it is not, then I don't see how it could work well... As far as I understand, all experimental environments are deterministic. So the algorithm description would clearly need to be rewritten, and the authors have to discuss the assumptions they are doing mainly: deterministic environments and also the fact that the "options" can only be extracted once a first policy has be learned (or by using expert traces) which limits its applicability.
In terms of experiments, the assumption made is that we have access to a set of 'good' trajectories (which is easy in the proposed environments, but may be difficult in the real-life). It is compared to the option-critic architecture which simultaneously learns the options and the policy and I think that the comparison is somehow unfair. Since SSC is more a "sequence compression" algorithm, I would prefer to compare with existing sequence compression algorithms like hierarchical recurrent neural networks for instance.  The results are illustrated in very simple environments and the article would gain by using more complex ones (for instance the Atari grand challenge dataset could be used for such a study). So it is difficult to understand if the approach as it is is really interesting and efficient for general RL purposes. 
Summary: A good idea, but not well described, with strong assumptions not discussed, and with low-quality experimental results. 
Some other minor remarks:
The introduction is a little bit messy and does not well allow one to understand the focus on the paper, mixing some notions of neuroscience with classical reinforcement learning aspects, the connection between the two domains being not trivial. 
Equation 2 versus Equation 3: What is the difference?
s notation appears in 2.1 and 2.2 while it corresponds to different things. The variables are not defined and we don't know in which domain they rely on. 
Articulation between sparse coding and MDL not clear (since sparse coding is directly a way to minimize the MDL). MDL never used after that.
section 3, paragraph 3: I do not understand what is described here. The description has to be rewritten to allow the readers to understand the algorithm e.g "the size of the dictionary elements is set to 2-timesteps. " ?  "The dictionary element a which has the highest explained variance is then selected and assigned an integer code n + 1 " Variance on what ?  what is T_i ?
[cite] appears in the introduction